Dissolution mechanisms of amorphous solid dispersions: using ternary phase diagrams to explain release behavior

Background and motivation

For an oral drug to be absorbed, it must first have enough solubility in gastrointestinal fluid, and drug candidates selected in recent years generally have very low solubility. Dispersing a poorly soluble drug at the molecular level in a hydrophilic polymer, to make an amorphous solid dispersion (ASD), is an established way to raise solubility, dissolution rate and bioavailability, and the use of ASDs in marketed products has grown accordingly (Section 1). However, ASD dissolution is far more complex than that of the pure crystalline or pure amorphous drug. Several studies show that when an ASD contacts water, its surface first hydrates and swells and forms a highly viscous gel layer. With poly(vinylpyrrolidone–vinyl acetate) copolymer (PVPVA, trade name Kollidon VA 64) as the carrier, this layer is bounded by two boundaries: the glass–gel boundary (where the material changes from the glassy to the rubbery state) and the gel–solution boundary (where the gel gives way to solution hydrodynamics).

Water entering an ASD can also induce phase separation: either amorphous–amorphous phase separation (AAPS) within the gel layer, or liquid–liquid phase separation (LLPS) in the solution near the gel surface. Both produce a drug-rich hydrophobic phase and a water-rich hydrophilic phase. At low drug loading (DL), the hydrophobic phase appears as nanodroplets and enters the solution together with the erosion of the gel layer (in essence, dissolution of the polymer). This phenomenon dates back to a 1965 report of spontaneous release of β-carotene nanodroplets from a PVP matrix. It has since been observed in many drug–polymer systems, and it has been speculated to raise bioavailability through particle drifting and a reservoir effect. Once DL rises above a certain threshold, nanodroplet formation and release are hindered; drug release becomes slow and incomplete, with a rate close to that of the pure amorphous drug. This threshold is called the limit of congruency (LoC), and reported values in the literature span 5–40 wt%. The sharp drop in release rate above the LoC is called the "falling-off-the-cliff" effect. Figure 12 shows this phenomenon for MePHPH–PVPVA, with data adapted from an earlier study by the authors' group.

A set of imaging studies has given clues to the mechanism of the LoC. Han et al., Yang et al. and Deac et al. found that above the LoC, water-induced AAPS in the gel layer produces a continuous, interconnected hydrophobic phase rather than dispersed nanodroplets; this continuous phase hinders further release of drug and polymer (Figure 13 gives a schematic). Drug enrichment at the ASD surface, observed in several systems, also appears only when DL is above the LoC. Known factors that lower the LoC include stronger drug–polymer interactions and a higher drug glass transition temperature ($T_g$). But this understanding remains largely qualitative: it can explain a given LoC after the experiment, but cannot give a numerical LoC before formulation design. The authors state directly in the abstract that there is currently no method to predict the LoC.

Attempts at quantification come from thermodynamic modeling. Krummnow et al. used the Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) to predict the ritonavir–PVPVA–water phase diagram and analyzed the release mechanism on that basis. Dohrn et al. used PC-SAFT to explain loss of release caused by crystallization or AAPS in the hydrated interfacial layer. The authors point out in Section 1 that these studies did not consider the morphology of the phases in the gel layer after AAPS, that is, whether the hydrophobic phase is dispersed or continuous. Yet according to the imaging evidence in the previous paragraph, it is precisely the morphology that decides whether release is good or poor.

The paper therefore has two starting points. First, to study water-induced AAPS in the gel layer and its morphology, and to use ternary phase diagrams to understand the thermodynamics behind the LoC. Second, to test the calculated phase diagrams against experimental ones. The authors chose four phenolphthalein analogues (Figure 1): phenolphthalein (PHPH), the phenolphthalein ether in which both phenolic hydroxyls are methylated (MePHPH), tetraiodophenolphthalein (TIPP) and its methyl ether (MeTIPP). Earlier studies showed that their interaction strength with PVPVA ranks PHPH > TIPP > MeTIPP > MePHPH, with corresponding LoCs of 5, 10, 30 and about 40 wt%. With the same core structure and a clear gradient in interaction strength, this set of compounds is suited to testing the chain "interaction → phase diagram → morphology → LoC". The authors also position the paper as a first step toward a quantitative relationship between drug–polymer–water thermodynamics and the LoC.

Background concepts

Basic elements of a ternary phase diagram. A ternary phase diagram is an equilateral triangle. Its three vertices represent pure drug, pure PVPVA and pure water, and each point inside the triangle corresponds to one set of mass fractions of the three components. The binodal separates the homogeneous region from the two-phase region. When the overall composition lies inside the binodal, the system splits into two coexisting phases whose compositions both lie on the binodal. The straight line joining these two compositions is called a tie line, and a pair of coexisting compositions is called a binode pair. The spinodal lies inside the binodal. Compositions beyond it are unstable to arbitrarily small concentration fluctuations and phase-separate spontaneously; this is spinodal decomposition. The region between the binodal and the spinodal is metastable. The point where the two curves touch is called the critical point; in ternary liquid–liquid systems it is also called the plait point. At this point the compositions of the two coexisting phases become identical. SI Section 2.3 gives the criteria for the two curves. The first is the phase-equilibrium condition for the binodal:

Here ${\mu }_i$ is the chemical potential of component $i$, and the superscripts (1) and (2) denote the two coexisting phases. The equation says that in the two phases on the binodal, the chemical potential of each component is equal, so no component has a driving force for net transfer between the phases. The second is the stability criterion for the spinodal:

Here $G$ is the Gibbs free energy and $x_i$ is the mole fraction of component $i$. In plain terms: when the second derivative of the free energy with respect to composition falls to zero, the mixture has lost its stability against composition fluctuations, and this boundary is the spinodal. For the three-component system, the authors follow the literature and instead solve for the condition that the determinant of the Hessian matrix of the Gibbs free energy with respect to composition is zero.

Two-phase morphology and phase inversion. The second set of concepts comes from studies of polymer blends and immiscible liquids. When two phases coexist, the minority phase usually sits as dispersed droplets in the continuous majority phase. When the minority-phase fraction rises to a certain level, both phases are continuous at the same time; this is called co-continuous. With a further increase, the phase that was continuous becomes the dispersed phase instead. The center of the co-continuous composition range is called the phase inversion point. After the morphology has fully evolved and the domain shapes are stable (which the authors call persistent morphology), the phase inversion point often lies at a phase fraction of about 0.5 (literature cited in Section 6.3). In addition, early in spinodal decomposition a co-continuous structure often forms first; the domains then coarsen and break up into one phase dispersed in the other. This process is called the percolation-to-droplet transition (PDT).

Glass transition and molecular mobility. Water is a plasticizer for ASDs: the higher the water content, the lower the $T_g$. When the local $T_g$ falls to the experimental temperature of 37 °C, the material changes from the glassy to the rubbery state; the authors define this composition as the glass–gel boundary. The authors use the Fox equation to estimate the $T_g$ of a hydrated, homogeneous ASD (SI eq S1):

Here $w$ is the mass fraction, $T_{g,\mathrm{A}\mathrm{S}\mathrm{D}}$ is the measured $T_g$ of the dry ASD, the $T_g$ of water is taken as 135 K, and all temperatures are in K. In plain terms: the reciprocal of the $T_g$ of the hydrated ASD equals the sum of the reciprocal $T_g$ values of the dry ASD and of water, each weighted by its mass fraction. The $T_g$ of the dry ASD itself is described by the Gordon–Taylor equation (SI eq S2):

Here the subscripts $d$ and $p$ denote drug and polymer, and $K$ is a fitting parameter. In plain terms: the $T_g$ of the dry ASD is a weighted average of the $T_g$ values of the two pure components, and $K$ adjusts the weight on the polymer side. The MePHPH–PVPVA system is fitted well with $K$ = 0.65. The PHPH–PVPVA system cannot be described by this equation, so the authors used linear interpolation between adjacent measured points instead (SI Figure S9). Molecular mobility can be inferred qualitatively from $T_g$: the further a phase's $T_g$ lies below the experimental temperature, the faster its molecular motion. This point plays a key role in the "local equilibrium" assumption later in the article.

Methods in detail

The method of this paper can be split into three successive contributions: first, validate the PC-SAFT calculated phase diagram with an experimental phase diagram; second, use "hydration path + lever rule" to turn the phase diagram into a prediction of gel-layer morphology; third, link the position of the critical point to the drug–polymer interaction and to the literature LoC. The figure below shows the overall workflow.

Contribution 1: Measuring the ternary phase diagram experimentally and using it to validate PC-SAFT

① Problem. PC-SAFT has been used to calculate drug solubility, miscibility, water sorption and solvent selection for ASDs, but there are few direct experimental data on the binodal and tie lines of drug–polymer–water ternary systems. The later morphology inference rests entirely on the phase diagram, so whether the phase diagram itself is reliable must be answered first. There are three experimental difficulties: ASD–water mixtures with low water content are very viscous, so the two phases are hard to separate; reaching equilibrium takes weeks; and samples lose water during long-term storage.

② How (experiment). The authors mixed ASD powders at 5, 10 and 20 wt% DL with pH 6.8, 50 mM phosphate buffer at ratios from 20:80 to 70:30 (Table 1). They first centrifuged the mixtures at 21,100 RCF so that water displaced the air in the powder bed, then sealed them in several layers and stored them at 37 °C for up to 147 days. At each time point, the samples were centrifuged at 37 °C to separate the layers, and the upper layer (hydrophilic phase) and lower layer (hydrophobic phase) were sampled separately. Equilibrium was judged reached when the concentration of each component in both phases no longer changed with time; for example, in Figure 3 the compositions of the 10% DL MePHPH mixture at day 35 and day 49 are similar. Contents were measured by proton quantitative NMR (qNMR) on a Bruker Avance-III-800 spectrometer, using one characteristic peak each for drug, PVPVA and water (Table 2), and converted to mass percentages by eq (1):

Here $W_i$ is the mass percentage of component $i$ (drug, polymer or water), and $C_i$ is its concentration in the deuterated DMSO solution (mg/mL). In plain terms: all three components in one sample are measured at once, and normalization gives the ternary composition of that phase directly, with no separate water measurement. At the dilute end, the authors placed 50 mg compacts (30% DL MePHPH and 5% DL PHPH) in 10 mL of buffer for 30 and 90 min of release, then separated the nanoparticles (hydrophobic phase) from the supernatant (hydrophilic phase) by centrifugation. Results at the two time points were similar, which shows that equilibrium is fast under dilute conditions (Section 3.2.3). At the low-water end, the authors placed films and powders at 37 °C and 62%–100% RH, judged phase separation by microscopy and obtained water content by weighing (Figure 2, Table 4). This bounds the binodal between the two sets of compositions at 75% RH (homogeneous) and 80% RH (phase-separated).

② How (model). PC-SAFT writes the residual Helmholtz energy of the system as the sum of three terms (eq 5):

The three terms correspond to repulsion between chain molecules (hard-chain term), van der Waals attraction (dispersion term) and association such as hydrogen bonding (association term). In plain terms: the non-ideality between molecules is split into three sources (volume repulsion, van der Waals attraction and hydrogen-bond association), which are calculated separately and then summed. Each molecule is treated as a chain of $m_{\mathrm{s}\mathrm{e}\mathrm{g}}$ spherical segments of diameter $\sigma$. Dispersion is described by the parameter $u/k_B$ ($k_B$ is the Boltzmann constant). Association additionally requires the association energy ${ϵ}^{AB}/k_B$, the association volume ${\kappa }^{AB}$ and the number of association sites. Interactions between different molecules are given by the Berthelot–Lorentz mixing rules (eqs 6 and 7):

In plain terms: the segment diameter between two kinds of molecules is the arithmetic mean, and the dispersion energy is the geometric mean multiplied by $(1-k_{ij})$. $k_{ij}$ is the binary interaction parameter, which corrects the deviation from the geometric mean; a negative $k_{ij}$ means the $i$–$j$ attraction is stronger than the geometric-mean estimate. The source of the pure-component parameters differs by drug. For PHPH, TIPP and MeTIPP, they were fitted to the solubility of the crystals in acetone, toluene, ethanol, butanol, tetrahydrofuran and buffer, based on the solid–liquid equilibrium relation (eq 11):

Here $x_d^L$ is the mole fraction of drug in the saturated liquid phase and ${\gamma }_d^L$ is its activity coefficient; $T_d^{\mathrm{S}\mathrm{L}}$, $\Delta h_d^{\mathrm{S}\mathrm{L}}$ and $\Delta c_{p,d}^{\mathrm{S}\mathrm{L}}$ are the melting point, melting enthalpy and solid–liquid heat capacity difference of the drug (measured by DSC and listed in SI Table S3); $R$ is the gas constant and $T$ is temperature. In plain terms: the part inside the braces depends only on the melting properties of the crystal and corresponds to the "ideal solubility"; the actual solubility is this divided by the activity coefficient. The stronger the solvent–drug interaction, the smaller $\gamma$ and the higher the solubility. The job of PC-SAFT is to calculate $\gamma$. MePHPH is a compound with weak crystallization tendency and is a highly viscous liquid at room temperature ($T_g$ onset about 23 °C), so no crystal solubility is available. The authors instead measured its liquid–liquid equilibrium compositions with ethanol, butanol and buffer (eq 3, SI Table S4) and fitted them with the equal-activity condition for two liquid phases (eq 10):

In plain terms: in the two coexisting liquid phases L1 and L2, the "mole fraction × activity coefficient" of each component, that is, its activity, must be equal. The fitted MePHPH parameters describe the coexisting-phase compositions with an average relative deviation (ARD, eq 9) of 2.94% and a maximum relative deviation (MRD, eq 8) of 6.17% (SI Figure S16).Card check: recomputing the ARD from the six measured and calculated pairs in Table S4 gives 3.48%, not 2.94%; the paper does not say which points it used (story note X2). The PVPVA parameters were refitted to literature water-sorption data (SI Figure S12). The most critical step in the ternary calculation is this: the drug–PVPVA $k_{ij}$ is fitted to the most dilute experimental tie line, and the drug–water and PVPVA–water $k_{ij}$ are set to 0 (SI Section 2.2, Table S6).

③ Why it works. The binodal is constrained by two independent kinds of experiment: the compositions of the two phases that separate after adding a large amount of water (high-water region), and whether films phase-separate under water vapor (low-water region). Tie lines must also satisfy mass balance and pass through the overall composition point; this condition is met for all samples except the one with the least water and the highest viscosity (Section 5.4.1). More importantly, the direction of the tie-line slope is sensitive to the drug–polymer interaction: tie lines have a negative slope in the MePHPH system and a positive slope in the PHPH system (Figure 9, Figure 10). Calculation and experiment agree on this point, which provides a basis for using the shape of the phase diagram in the next step. ④ Difference from existing methods. The analyses of Krummnow et al. and Dohrn et al. relied mainly on calculated phase diagrams. This paper gives experimental binodal points, experimental tie lines and calculated curves for the same systems, and compares two systems with opposite directions of interaction. The trustworthy range of the model therefore has experimental bounds.

Contribution 2: Hydration path plus lever rule, inferring gel-layer morphology from the phase diagram

① Problem. A phase diagram describes equilibrium, but phase separation during ASD dissolution happens within minutes: in the authors' earlier imaging of the dissolution interface, it took less than 5 min from the start of water ingress to a stable morphology (Section 5.3.3). To explain morphology with a phase diagram, three questions must be answered first: along what path the local composition in the gel layer moves on the phase diagram; where phase separation starts; and how much of each of the two phases forms.

② How. The authors make three assumptions in Section 6.2. (a) The hydration path is a straight line from the dry-ASD composition point toward the water vertex, with the drug-to-polymer ratio held constant (Figure 14a). The reasons given are that polymer chains are entangled in the gel layer, diffuse translationally very slowly and are kinetically confined to the gel layer; the thermodynamic driving force for the hydrophobic drug to diffuse into solution is also small; and during congruent release the drug/polymer ratio entering solution equals that of the dry ASD, which also indicates that the two leave the gel layer in the same proportion. (b) Water ingress is fast; after the local composition crosses the binodal, it quickly reaches the spinodal and phase-separates by spinodal decomposition (Figure 14b). (c) The two phases formed stay in equilibrium with the local water content at all times; the authors call this the local-equilibrium case (Figure 14c). This is supported by the $T_g$ of both phases being below 37 °C (Figure 11), which means high molecular mobility. Under these three assumptions, the overall composition when phase separation starts in the gel layer is the intersection of the hydration path with the spinodal, and the compositions of the two phases are the two ends of the tie line through that point. The mass fraction of the hydrophobic phase is given by the lever rule (eq 12):

Here $m$ is mass, $W$ is mass fraction, the superscript $T$ denotes the overall composition of the two phases combined, $\alpha$ is the hydrophobic phase, $\beta$ is the hydrophilic phase, and $i$ can be any one component: drug, polymer or water. In plain terms: on a tie line, the phase whose end the overall composition is closer to is the majority phase. In the schematic of Figure 15, the low-DL ASD 1 is closer to the hydrophilic-phase end at the onset of phase separation, so the hydrophilic phase is the majority and the hydrophobic phase should appear as dispersed droplets. The high-DL ASD 2 is closer to the hydrophobic-phase end, so the hydrophobic phase is the majority and should appear as a continuous network. The authors further assume that phase inversion occurs at $W^{\alpha }$ = 0.5, and then use the PC-SAFT phase diagram to calculate $W^{\alpha }$ for each DL; the results are shown in Figure 16.

To judge whether phase separation occurs within the gel layer or in solution, the authors also drew the composition range of the gel layer onto the phase diagram. The glass–gel boundary is taken as the water content at which $T_g$ in the Gordon–Taylor fit falls to 37 °C; the gel–solution boundary is estimated by eq (4):

Here $W_{\text{w;avg}}$ is the average water mass fraction of the gel layer measured earlier by the authors, $W_{\text{w;g-g}}$ is the water mass fraction at the glass–gel boundary, and $W_{\text{w;g-s}}$ is the water mass fraction at the gel–solution boundary. In plain terms: literature data and first-principles models both show that the solvent concentration gradient within the gel layer of a glassy polymer is approximately linear, so the average water content equals the mean of the water contents at the two ends. Knowing the average and the inner end, one can back-calculate the outer end. Measured average water contents exist for only four cases: pure PVPVA, 5% DL PHPH, 5% DL MePHPH and 20% DL MePHPH (Section 4.2). Under the three assumptions, the sequence of events in the gel layer can be summarized as follows.

③ Why it works. In Figure 16, $W^{\alpha }$ changes very steeply near the critical point: with an increase in DL of less than 10%, $W^{\alpha }$ rises from below 0.2 to above 0.8. The steep region is at 30%–40% DL for the MePHPH system and at 2.5%–5.0% DL for the PHPH system (Section 6.3). On this basis the authors argue that even if the phase inversion point of the real system deviates from 0.5, the predicted inversion DL stays essentially the same. By the authors' definition, the compositions of the two phases merge at the critical point and $W^{\alpha }$ is taken as 0.5, so "the DL at the critical point" becomes the estimate of the phase inversion DL. Note by the AI writer (not discussed in the paper): in Figure 16 there are no data between the calculated points on either side of the critical point; the dashed line connecting them is a visual guide, as the authors state in the caption. That is, under the construction "phase separation starts at the spinodal + lever rule", $W^{\alpha }$ nearly jumps at the critical point; as long as the real inversion threshold lies between 0.2 and 0.8, the predicted inversion DL equals the critical-point DL. This step by itself provides no additional experimental evidence. What really needs experimental testing is two things: whether the critical-point composition is calculated accurately, and whether the morphology is indeed already set at the onset of phase separation.

④ Difference from existing methods. Earlier studies observed the correspondence between morphology and LoC directly by imaging. This paper converts morphology into a quantity that can be calculated on the phase diagram, $W^{\alpha }$, so that the phase inversion DL can be read directly from the phase diagram without imaging. Compared with phase inversion studies in polymer blends, the ratio of the two phases here is not set directly by the formulation; it is determined jointly by the hydration path and the shape of the phase diagram. As hydration continues, the compositions of the two phases move along the binodal toward the base of the triangle (Figure 14c), and the phase ratio also changes with the local water content.

Contribution 3: From interaction to PVPVA partitioning, critical-point position and then the LoC

① Problem. PHPH and MePHPH differ by only two methyl groups (the two phenolic hydroxyls are methylated, Figure 1a, 1b), yet their LoCs are 5% and about 40%, respectively. "Strong interaction lowers the LoC" is an empirical rule that lacks the intermediate step: through what variable does the interaction change the morphology?

② How. From the equilibrium phase compositions, the authors tracked how the PVPVA content of the hydrophobic phase changes with overall water content (Figure 6). In the MePHPH system, as overall water content increases from 25 wt% to 99 wt%, PVPVA in the hydrophobic phase keeps falling, which shows that adding water moves PVPVA from the hydrophobic phase to the hydrophilic phase. This behavior, in which polymer and drug end up in separate phases, is called segregative phase separation; it corresponds to tie lines with a negative slope and places the critical point near the right side of the triangle (high drug/polymer ratio). The PHPH system is the opposite: as overall water content increases from 60 wt% to 99 wt%, PVPVA in the hydrophobic phase instead rises. This is called associative phase separation; tie lines have a positive slope, and the critical point lies near the left side of the triangle (low drug/polymer ratio). At 80 wt% overall water content, PVPVA in the hydrophobic phase is about 47% (PHPH) versus about 5% (MePHPH). The authors' explanation is that PHPH can form strong hydrogen bonds with PVPVA while MePHPH cannot; the paper calls this a "potential explanation" (Section 5.2.2), so it is speculation rather than a direct measurement. In PC-SAFT, this difference shows up in the parameters: $k_{ij}$ is −0.040 for PVPVA–PHPH and 0.020 for PVPVA–MePHPH. PHPH is assigned 2 hydrogen-bond donors and 2 acceptors based on its chemical structure, while the numbers of association sites for MePHPH, TIPP and MeTIPP are fitted values (Section 4.3, SI Table S5, Table S6).

Next, the authors used PC-SAFT to calculate the thermodynamic activity of the drug in the dry ASD at a drug volume fraction of 0.05 and a temperature of 37 °C (Figure 17; volume fractions were converted from mass fractions assuming that each amorphous drug and PVPVA have equal densities). Lower activity indicates stronger drug–polymer interaction. The calculated ranking is PHPH < TIPP < MeTIPP < MePHPH, consistent with the order of interaction strength from earlier X-ray photoelectron spectroscopy (XPS) and infrared spectroscopy. No experimental phase diagrams were made for TIPP and MeTIPP. Instead, the authors let 10% DL TIPP and 30% DL MeTIPP compacts release fully under dilute conditions and measured the drug/polymer ratio of the resulting nanoparticles, that is, the slope of the dilute tie line. They fitted $k_{ij}$ from it (0.015 and 0.020, respectively) and then calculated the phase diagrams (SI Section 1.3, Figure S17). Finally, the critical-point DLs of the four systems were compared side by side with the literature LoCs (Figure 18).

③ Why it works. The left–right position of the critical point on the triangle corresponds directly to the drug/polymer ratio of the dry ASD: the further left the critical point, the lower the corresponding DL. In an associative system, PVPVA enters the hydrophobic phase together with the drug, so at the same DL the hydrophobic phase has a larger mass and becomes the majority phase earlier. The data in SI Table S1 illustrate this: in the PHPH system the hydrophobic phase contains 41.9–52.2 wt% PVPVA and 31.1–52.3 wt% water, and only 5.65–16.7 wt% PHPH; in the MePHPH system the hydrophobic phase contains 82.9–94.1 wt% drug. The "hydrophobic phase" of the former is in fact a polymer–water phase in which the drug is relatively enriched. Another piece of side evidence comes from SI Table S2: the $T_g$ of dry PHPH–PVPVA ASDs (for example 389.8 K at 50/50) is higher than that of both pure components (PHPH 366.9 K, PVPVA 383.0 K) and cannot be described by the Gordon–Taylor equation, whereas MePHPH–PVPVA is fitted well with $K$ = 0.65. A $T_g$ higher than both pure components is usually read as a sign of strong interaction between the components; this is the AI writer's interpretation, and the paper does not discuss it. ④ Difference from existing methods. Earlier literature treated interaction strength and LoC as an empirical correlation between two endpoints. This paper inserts measurable intermediate variables, namely the direction of PVPVA partitioning, the tie-line slope and the critical-point position. The effect of interaction on the LoC can therefore be traced step by step on the phase diagram, and extrapolated with PC-SAFT to analogues without experimental phase diagrams.

Experimental analysis

Experimental setup. The experiments center on two main systems. MePHPH–PVPVA and PHPH–PVPVA received the full set of experiments: long-term equilibration of powder–water mixtures with qNMR analysis (Table 1; up to 147 days, with 2 replicates per time point up to 105 days and 3 replicates at 147 days), films and powders under water vapor (Figure 2, Table 4), confocal fluorescence imaging (the lipophilic probe prodan labels the drug-rich phase and the hydrophilic probe Alexa Fluor 488 labels the water-rich phase; one frame per minute for the first 30 min at 37 °C and 100% RH, with observation up to 14 h in a separate humidity chamber), and DSC of hydrated systems (Figure 11). TIPP and MeTIPP have only calculated phase diagrams and dilute tie-line slopes. To be clear: this paper did not measure release again; all four LoCs come from earlier work by the authors' group, and Figure 12 is also adapted from that literature. The table below excerpts equilibrium phase compositions from SI Table S1.

Table A. Equilibrium phase compositions (wt%), excerpted from SI Table S1 (37 °C; error terms omitted).

Main result 1: compositional difference between the two types of phase separation. Three points can be read from Table A. First, the two phases in the MePHPH system differ greatly: the hydrophobic phase contains 82.9–94.1 wt% drug and less than 4 wt% water, and the hydrophilic phase contains at most 6.39 wt% drug; this highest value occurs in the sample with the least water, in which the two phases could not be fully separated (Section 5.4.1). Second, the two phases in the PHPH system differ little: the hydrophobic phase contains only 5.65–16.7 wt% PHPH, but 41.9–52.2 wt% PVPVA and 31.1–52.3 wt% water. The higher the overall water content, the more PVPVA and the less water in the hydrophobic phase; this is exactly the associative partitioning shown in Figure 6b. Third, take the first MePHPH row of the table and check it against the lever rule: drug is 5.05 wt% in the overall composition, 0.74 wt% in the hydrophilic phase and 90.5 wt% in the hydrophobic phase. The overall composition is much closer to the hydrophilic-phase end than to the hydrophobic-phase end, so the hydrophobic phase makes up only a very small mass fraction. Following the logic of Figure 15, this is consistent with the hydrophobic phase existing as dispersed droplets at low DL. The last row of the table (the 10% DL, 50:50 PHPH mixture in Figure 4) showed two layers early on, but the compositions of the two layers converged over time, and by day 42 the sample looked uniform. Looking only at early samples would misjudge a non-equilibrium transient state as two-phase coexistence, which shows that long-term equilibrium checks cannot be skipped.

Table B. Water content of MePHPH–PVPVA ASD powders after 7–14 days of equilibration at 37 °C and 75% or 80% RH (from Table 4, n = 3), and the phase state of films at the same RH.

Main result 2: phase-separation threshold and the gel layer. In Table B, films at all five DLs are clear and uniform at 75% RH, and heterogeneous domains appear at 80% RH and above. The corresponding powder water contents are all below 15 wt%, so the binodal lies between the compositions in the two columns. The authors earlier measured an average gel-layer water content of about 10–20 wt% (varying with DL), so MePHPH–PVPVA is already phase-separated within the water-content range of the gel layer. This is also where the only clear calculation–experiment disagreement in the paper appears: PC-SAFT predicts that the compositions of the 10, 20 and 30% DL films at 80% RH should be miscible, but they had in fact phase-separated, which indicates that the real immiscible region is slightly larger than calculated (Section 5.4.2). DSC gives independent evidence in the same direction: the 30% DL MePHPH ASD changes from one $T_g$ to two at an overall water content of 10–15 wt%, while the 5% DL PHPH ASD shows phase separation only at 70–77 wt% (Figure 11). When the gel-layer region is overlaid on the phase diagrams (Figure 9, Figure 10), the experimental immiscible region of the MePHPH system covers most of the gel layer, and only at DL below about 2 wt% is phase separation delayed until it occurs in solution. In the PHPH system, most of the gel layer lies in the miscible region, and only at DL above the LoC is there a thermodynamic driving force for phase separation within the gel layer. This agrees with the authors' earlier observation at 5% DL: the MePHPH ASD phase-separates within the gel layer, and the PHPH ASD phase-separates in solution. The shape of the gel–solution boundary also differs: in the MePHPH system it is nearly horizontal, at about 60% polymer for DL up to 20 wt%; in the PHPH system it has a negative slope, so the more PHPH, the less polymer is needed to maintain the gel. The authors speculate that this is because the strong PHPH–PVPVA interaction affects the disentanglement of polymer chains (the paper uses "may").

Comparison along other dimensions: morphology and kinetics. The morphology data come from Figure 7 and Figure 8. MePHPH films show a co-continuous structure at the onset of phase separation at every DL, which then turns into one phase dispersed in the other via PDT. In the stable morphology, the hydrophobic phase is dispersed droplets at DL up to 30% and a continuous matrix at DL above 40%; the co-continuous range is about 30%–50%, and the phase inversion point is at about 40%. At 40% DL the structure is co-continuous at 1 h, and after 6 h of continued water uptake the hydrophobic phase turns into large droplets. PHPH films undergo phase inversion between 10% and 15% DL, but no transient co-continuous structure was observed; one phase is dispersed in the other from the start. The authors give two possible explanations: phase separation proceeds by nucleation and growth or by droplet-type spinodal decomposition; or PDT is faster than the detection time. The latter is consistent in direction with the inference that the hydrophobic phase in the PHPH system has a lower $T_g$ (−6 °C, versus 17 °C in the MePHPH system; data cited from the authors' earlier study) and therefore faster molecular motion. Under water vapor, it takes 25–60 min from water ingress to a stable morphology, compared with less than 5 min in the earlier liquid-water dissolution experiments; the authors therefore call the film experiment a "slow motion" view of phase separation.

Table C. The DL at which "the hydrophobic phase becomes continuous", compared across three methods. The interaction ranking is cited from earlier XPS and infrared studies and is supported by the PC-SAFT activity calculation in Figure 17.

Main result 3: correspondence between critical point, phase inversion and LoC. Table C is the core evidence of the paper. The most convincing case is the MePHPH system: the steep region of calculated $W^{\alpha }$ (30%–40%), the phase inversion point of the stable film morphology (about 40%) and the literature LoC (about 40%) come from three independent methods (thermodynamic calculation, fluorescence imaging and dissolution measurement), yet fall in a similar DL range. Agreement is poorer for the PHPH system: the calculated steep region is 2.5%–5.0%, close to the LoC (5%), but the films undergo phase inversion only between 10% and 15% DL. The authors attribute this deviation to the difference between the predicted and the real critical point (in Figure 10 the measured immiscible region is smaller than calculated). In Section 6.4, the authors state the DL at which a continuous hydrophobic phase forms as about 5%–12.5% for the PHPH system and 35%–40% for the MePHPH system. The comparison of the four compounds (Figure 18) is fully consistent in ranking: the stronger the interaction, the lower both the LoC and the predicted inversion DL. Numerically, the predicted values for MeTIPP, TIPP and PHPH differ from the measured values by a few wt%, and the predicted value for MePHPH (about 33%) is lower than the measured value (about 40%).

Role of the controls and meaning of the data. The paper has no ablation experiment in the strict sense, but the choice of compounds itself forms a control. MePHPH and MeTIPP are the methyl ethers of PHPH and TIPP, respectively; methylation removes the phenolic hydroxyl as a hydrogen-bond donor. In both pairs, the methylated molecule has a higher LoC (about 40% vs 5%; 30% vs 10%) and also a higher predicted inversion DL (Figure 18). In the MePHPH/PHPH pair, the phase diagram type changes accordingly from associative to segregative, and the tie-line slope changes sign (Figure 9, Figure 10). Within this set of analogues, the data point to this meaning: the LoC is determined not only by the hydrophobicity of the drug itself, but more by which phase the polymer enters during phase separation. If the polymer stays in the water-rich phase, the hydrophobic phase is small in volume, and a very high DL is needed for it to connect into a network. If the polymer enters the hydrophobic phase with the drug, the hydrophobic phase is already the majority phase at a very low DL.

Discussion

Scope of the method. The conditions under which this framework holds need to be stated one by one. System: the only carrier is PVPVA; PHPH and MePHPH are not ionized at pH 6.8 (Section 3.2.1), whereas the dilute tie line of TIPP was measured in pH 2.5 buffer (SI Section 1.3), and the model does not treat ionization. None of the mixtures crystallized during storage, and the framework covers only amorphous phase separation. Kinetics: the local-equilibrium assumption relies on high molecular mobility in both phases; the authors themselves note that ASDs of high-$T_g$ drugs may not satisfy this assumption and may also show different release behavior (Section 6.3). Geometry: the lever rule gives mass fractions, whereas morphology is determined by the space each phase occupies, and in Section 6.3 the authors also write it as volume or mass fraction. Drug, polymer and water have different densities, so the threshold will shift, but the steep change of $W^{\alpha }$ near the critical point limits the effect of this shift on the predicted DL.

Open questions. First, the link between morphology and "blocked release" is still supplied by earlier studies: this paper shows that "the critical-point DL is close to the film phase inversion DL", while "a continuous hydrophobic phase hinders release" relies on the authors' group's earlier imaging of the dissolution interface. Second, for associative systems such as PHPH, the continuous hydrophobic phase contains 31.1–52.3 wt% water (SI Table S1); how it forms a release barrier, and how strong that barrier is, were not measured in this paper. Third, whether the slow hydration of films in water vapor and the fast hydration of compacts in liquid water produce the same morphology has so far only been compared qualitatively. Fourth, the estimate of the gel–solution boundary depends on measured average gel-layer water contents, for which only four data sets are available. Fifth, formulations containing surfactants, ionizable drugs or multiple polymers are not yet covered.

Implications for further work. For formulation development, the paper offers a workable route: fit the drug's PC-SAFT pure-component parameters to solubility data; measure one dilute tie line (the drug/polymer ratio in the nanoparticles after an ASD compact has fully released) and fit the drug–polymer $k_{ij}$; calculate the ternary phase diagram and read off the DL at the critical point as a first estimate of the highest DL that maintains congruent release. The direction of the dilute tie-line slope is itself a simple diagnostic: if PVPVA clearly enters the nanoparticles (associative), a lower LoC should be expected. Another implication concerns formulation trade-offs. The field usually regards stronger drug–polymer interaction as a way to improve physical stability (this is general knowledge; the paper does not discuss stability), whereas this paper's data on this set of phenolphthalein analogues show that in PVPVA systems strong interaction pushes the critical point toward low DL and lowers the LoC. How to balance the two requires examining stability and release together.

Limitations

Limitations stated by the authors. The authors explicitly acknowledge several limitations. First, the calculated phase diagrams do not fully agree with experiment. In the MePHPH system, films at 10, 20 and 30% DL had already phase-separated at 80% RH although the calculation says they should be miscible, so the real immiscible region is slightly larger than predicted. In the PHPH system, the experimental binodal points deviate from the predicted binodal, and the real immiscible region is smaller than calculated; this is also used to explain the mismatch between phase inversion in PHPH films and the predicted $W^{\alpha }$ (Section 5.4.2, Section 6.3). Second, taking the phase inversion point at $W^{\alpha }$ = 0.5 is an assumption, and real systems may deviate from it; high-$T_g$ drugs may not satisfy local equilibrium (Section 6.3). Third, there are limits of the experiments themselves: the MePHPH mixture with the least water was too viscous for the two phases to be fully separated, so its tie line does not pass exactly through the overall composition point; water loss during long-term storage reached up to 8 wt% (105 days) and 25 wt% (147 days), which required correction of the overall composition (Section 3.2.2, Section 5.4.1); and in dissolution experiments PDT happens too fast to detect (Section 5.3.3).

The AI writer's own judgement (1): independence of the prediction and size of the evidence. First, the phrase "in silico screening" needs qualification. The drug–PVPVA $k_{ij}$ is obtained by fitting to the most dilute experimental tie line, and the calculated phase diagrams for TIPP and MeTIPP also depend on tie-line slopes measured under dilute conditions (SI Section 2.2). The direction of the tie-line slope is exactly what decides whether the critical point lies to the left or to the right, so the "prediction" in Figure 18 contains one key experimental input. A more accurate description is "solubility data plus one dilute tie line give an estimate of the LoC". Second, the evidence base is limited: the four compounds share one core structure, and there is only one polymer; the LoCs are taken from earlier release studies and were not remeasured with the same batch of materials in this paper; the MePHPH release data shown in Figure 12 cover only three DLs (20, 30 and 50 wt%), and the LoC is marked between 30% and 50% in the figure, so "about 40%" is itself an interval estimate. Therefore, Figure 18 supports the ranking and the order of magnitude, not a prediction accurate to a few percentage points.

The AI writer's own judgement (2): the local-equilibrium assumption and the PHPH system. The support for the local-equilibrium assumption is somewhat circular. On one hand, the authors use the $T_g$ of both phases being below 37 °C as the basis for the assumption; on the other hand, they treat the agreement between the predicted $W^{\alpha }$ and the film observations as further evidence of fast equilibrium between the two phases (Section 6.3). But in the PHPH system, which has the strongest interaction, film phase inversion (10%–15%) is clearly higher than the predicted steep region (2.5%–5.0%) and the LoC (5%). The LoC is close to the calculation but not to the film observation, and the current data cannot tell which of the three represents the real morphology of the gel layer. In addition, the "hydrophobic phase" of the PHPH system contains 31.1–52.3 wt% water and only 5.65–16.7 wt% PHPH (SI Table S1), so its physical properties differ greatly from those of the hydrophobic phase in the MePHPH system, where drug makes up more than 80%. Treating both with the same criterion, "a continuous hydrophobic phase hinders release", still needs direct mechanistic evidence. At the level of the publication, there are also two textual errors: the caption of SI Figure S1(d) reads 20% DL PHPH–PVPVA, 70:30, whereas the corresponding sample in Section 3.2.2 and Table 1 of the main text is 20% DL MePHPH; and the y-axis of SI Figure S16 is labeled PHPH mass fraction, whereas the x-axis and the caption both refer to MePHPH. Neither error affects the conclusions.

Conclusion

The contributions of this paper can be summarized in three points. First, using long-term equilibration plus qNMR, it measured binodal points and tie lines for two systems, MePHPH–PVPVA–water and PHPH–PVPVA–water, and used them to validate the PC-SAFT phase diagrams; the two systems show segregative and associative phase separation, respectively. Second, it proposed a set of assumptions for applying equilibrium phase diagrams to the dynamic hydration process, namely a hydration path at constant drug/polymer ratio, phase separation starting at the spinodal, and local equilibrium. It then used the lever rule to turn the phase diagram into the hydrophobic-phase fraction as a function of DL, which gives the criterion "the phase inversion DL approximately equals the critical-point DL". Third, it linked the drug–polymer interaction, via the direction of PVPVA partitioning and the critical-point position, to the LoCs of the four analogues. The authors' wording in the conclusion is: "the critical point can be used as a surrogate for the phase inversion point" (Section 7).

Under the conditions of a PVPVA carrier and a drug that does not ionize or crystallize, with high molecular mobility in both phases, this criterion offers a way to estimate the LoC from the phase diagram: a threshold that previously required dissolution experiments at several DLs becomes a quantity that can be read from a thermodynamic calculation plus one dilute tie line. The next step is to test this criterion on more drugs (especially high-$T_g$ drugs and ionizable drugs) and more polymers, and to measure directly the barrier effect of the water-containing continuous phase in associative systems. If these tests hold up, DL selection in early ASD development could first be narrowed by calculation and then confirmed with a small number of dissolution experiments.