How much drug can molten PEG hold? Testing a Flory–Huggins eutectic model on four drugs

Background and motivation

Many drug candidates from high-throughput discovery are large and lipophilic and dissolve poorly, so oral delivery often needs a formulation that raises the dissolution rate (Lipinski et al., ref 1). Dispersing the drug in a polymer, a solid dispersion, is one of the most common approaches (refs 2–9). The authors separate two kinds. In an amorphous solid dispersion the amorphous drug is blended with an amorphous polymer; these have been studied widely, but few marketed products use them, partly because of worries about long-term physical instability (refs 10–18). C2 In a crystalline solid dispersion the drug stays crystalline inside a usually crystalline polymer such as polyethylene glycol (PEG).

Crystalline dispersions come in two types. In both, drug and polymer mix completely as liquids and hardly at all as solids; they differ in how much crystalline drug the molten polymer can dissolve. In a monotectic system the drug barely dissolves in the melt and does not noticeably lower the polymer's melting point. In a eutectic system it dissolves appreciably, and the eutectic point marks the most drug the molten polymer can hold, at the eutectic temperature. C1 That makes the eutectic composition a practical limit: a eutectic dispersion is feasible only if the dose fits under it (Law et al., ref 19). Finding the eutectic by experiment means building the drug–polymer phase diagram, which costs time and material, so a quick estimate is attractive. C3

Several semi-empirical models estimate the eutectic composition from the molecular weight, melting point, heat of fusion and molar volume of drug and polymer, "with varying success" (refs 19–22). PEG, which is water-soluble, melts low and is non-toxic, is a favoured carrier (refs 23, 24), so a model that tells quickly whether useful drug loading in PEG is possible would be helpful. C4 Lacoulonche et al. built such a model by applying the Flory–Huggins lattice theory of polymer solutions to flurbiprofen in PEG 6000 (ref 25); it was later tested on flurbiprofen (ref 26) and other organic compounds in PEG (Vippagunta et al., ref 27). The authors note that it was "still debatable" which properties of drug or polymer make it go wrong; both the physical properties and the strength of specific drug–polymer interactions "potentially" affect the predicted eutectic. C5

The paper therefore asks two things: for which kind of drug the model's interaction term matters, and whether deviations from the ideal prediction are caused by specific drug–polymer interactions rather than by the model's other assumptions. The authors predicted the eutectic composition of four drugs in PEG 3350 with the interaction term set to zero, compared the predictions with measured phase diagrams, and then probed the drug–PEG interaction independently by solubility in liquid PEG 400 and by infrared spectroscopy of the melts. A1·P6·P5·P4

Background concepts

Reading a eutectic phase diagram

A binary phase diagram of drug and polymer plots, against composition, the temperature at which the last crystal melts on heating: the liquidus. Starting from pure PEG, adding drug lowers the PEG melting point along one branch; starting from pure drug, adding PEG lowers the drug melting point along the other. The two branches meet at the lowest point, the eutectic, where both solids melt together. Its composition is the eutectic composition. In a monotectic system the PEG branch is almost flat and the eutectic sits essentially at pure PEG. C1

The authors read their DSC traces in this frame. Away from the eutectic, a dispersion shows two endotherms: a low-temperature one, assigned to melting of the eutectic (or monotectic) composition, and a high-temperature one from the excess component, PEG below the eutectic and drug above it. Close to the eutectic composition only one endotherm appears, below the melting point of either pure component. C13 The liquidus temperature at each composition (the DSC offset temperature, or the temperature at which hot-stage microscopy shows the last solid particle melting) gives the experimental phase diagram. P2·P3

The Lacoulonche model

The model treats the melt as a Flory–Huggins polymer solution and writes one liquidus branch for each crystalline component. With ${\varphi }_d$ the volume fraction of drug, $\Delta H_{\mathrm{f}\mathrm{u}\mathrm{s},d}$ and $\Delta H_{\mathrm{f}\mathrm{u}\mathrm{s},p}$ the heats of fusion of drug and polymer, $T_{\mathrm{m}\mathrm{e}\mathrm{l}\mathrm{t},d}$ and $T_{\mathrm{m}\mathrm{e}\mathrm{l}\mathrm{t},p}$ their melting temperatures, $V_{\mathrm{m}\mathrm{o}\mathrm{l},d}$ and $V_{\mathrm{m}\mathrm{o}\mathrm{l},p}$ their molar volumes, $R$ the gas constant and $\Delta W_{d,p}$ the total interaction energy per macromolecular volume element between drug and polymer, the two branches are (Eqs. 1 and 2): E1·E2

In plain terms: this is the temperature at which crystalline drug is in equilibrium with a melt of drug fraction ${\varphi }_d$. At pure drug (${\varphi }_d=1$) it returns the drug's own melting point; diluting the drug with PEG lowers it, and a negative interaction energy lowers it further. E1

In plain terms: the same for crystalline PEG; at ${\varphi }_d=0$ it returns the melting point of PEG, and adding drug lowers it. The predicted eutectic composition is the drug fraction at which both equations give the same temperature. E2·P6 The text of the paper assigns Eq. 1 to compositions below the eutectic and Eq. 2 to compositions above it; since Eq. 1 ends at the drug's melting point and Eq. 2 at the polymer's, the physically meaningful pairing is the reverse, and the predicted lines in Figure 4 follow the equations, not the text labels (note by the AI writer, from the card's extractor notes). X1

Because the model works in volume fractions, the authors convert to weight fraction with Eq. 4, where $M_d$ and $M_p$ are the molecular weights: E4

In plain terms: since each molar volume is molecular weight divided by density (Table 1), this simply weights each volume fraction by the component's density. E4·M1

Interaction energy and the Flory–Huggins parameter

$\Delta W_{d,p}$ carries all the chemistry of drug–polymer contacts. When it is zero, mixing is athermal: drug–polymer contacts are as strong as drug–drug and polymer–polymer contacts. A negative value means exothermic mixing, with drug–polymer contacts stronger than the components' own; a positive value means endothermic mixing. For the predictions the authors set $\Delta W_{d,p}=0$, so only the crystal properties (melting point and heat of fusion) and the molar volumes enter. C6 When the eutectic composition ${\varphi }_{\mathrm{e}\mathrm{u}\mathrm{t}}$ is known from experiment, setting Eqs. 1 and 2 equal at that composition gives the interaction energy; the paper prints the result as Eq. 3, shown here exactly as printed except that its two repeated bracketed expressions are written as $A_p$ and $A_d$ (they are the denominators of Eqs. 2 and 1 at the eutectic): E3

In plain terms: the interaction energy is whatever value makes the two liquidus branches cross at the observed eutectic instead of at the athermal one. A larger miss between prediction and observation means a larger interaction energy. E3·C17

Note by the AI writer (not discussed in the paper). As printed, Eq. 3 does not follow from Eqs. 1 and 2: equating them and solving for $\Delta W_{d,p}$ gives a difference, not a sum, in the numerator and no heats of fusion multiplying the denominator terms, and the printed form returns a dimensionless number rather than an energy. The interaction energies in Table 2 are therefore best read as signs and a ranking; the card's recomputation is described with Table B below. X3

The authors then convert the interaction energy into the familiar Flory–Huggins interaction parameter ${\chi }_{dp}$ with the equation of Lacoulonche et al. (Eq. 8), where $T_{\mathrm{e}\mathrm{u}\mathrm{t},\mathrm{t}\mathrm{h}}$ is the melting temperature of the eutectic mixture predicted by the model: E8

In plain terms: ${\chi }_{dp}$ is the interaction energy in units of thermal energy at the eutectic temperature. Positive values mean endothermic mixing, zero athermal mixing and negative values exothermic mixing. E8·C26 The authors introduce Flory–Huggins theory as the version of solution theory that suits a polymer mixed with small molecules, because it treats the polymer as a chain of segments each the size of a solvent molecule instead of assuming components of similar size (Flory, ref 34; Huggins, ref 35). C26

The activity coefficient from solubility in a liquid analogue

A second, independent way to look for interactions is the activity coefficient ${\gamma }_d$ of the drug in the polymer. The solubility of a crystalline drug in a solvent follows the simplified solubility equation (Eq. 5), where $x_d$ is the mole-fraction solubility and $\Delta G_{\mathrm{f}\mathrm{u}\mathrm{s}}$ the free-energy difference between crystalline and liquid drug at temperature $T$ (refs 29, 30): E5

In plain terms: the stronger the crystal (the larger $\Delta G_{\mathrm{f}\mathrm{u}\mathrm{s}}$), the lower the solubility; ${\gamma }_d=1$ is the ideal case. E5 The free-energy difference is estimated from the melting data with the Hoffman equation (Eq. 6, ref 31): E6

In plain terms: the driving force for melting grows with the heat of fusion and with how far below its melting point the drug is held. E6 Combining the two gives the activity coefficient from a measured solubility (Eq. 7): E7

In plain terms: ${\gamma }_d$ is the ideal solubility divided by the measured one. Below 1, the drug dissolves better than ideal; since ${\gamma }_d$ reflects the entropy and/or enthalpy of mixing, a value well below 1 can signal specific drug–solvent interactions. E7·C20 Measuring ${\gamma }_d$ directly in a viscous, semicrystalline polymer like PEG 3350 is hard because of its high viscosity and the low vapour pressure of drug and polymer (Marsac et al., ref 32), so the authors measure solubility in PEG 400, a liquid, low-molecular-weight analogue, while noting that its end groups "may" make it chemically different. C21·C22

Seeing hydrogen bonds in infrared spectra

Infrared spectroscopy is widely used to detect drug–polymer interactions in dispersions (refs 36–46). Hydrogen bonding moves the bands of donor groups (NH, OH) and acceptor groups (C=O, C–N). The authors compare the spectrum of each molten 25:75 drug–PEG mixture with a calculated spectrum built from the spectra of pure molten PEG and pure molten drug in the same weight ratio (procedure of Rumondor et al., ref 47). A system without specific interactions should resemble the calculated spectrum, although a molten mixture always shows some differences from non-specific interactions. A carbonyl band that moves to higher wavenumber means that the carbonyl takes part in fewer hydrogen bonds than in the pure drug. C28·P4

Methods in detail

The study has three parts: a prediction with the interaction term switched off, a measurement of the real phase diagrams, and two tests for drug–PEG interactions that do not depend on the phase diagram. The flow below shows how they connect. A1

Contribution 1: predicting the eutectic with no interaction term

Problem. Can the eutectic composition be estimated from the physical properties of drug and polymer alone? What they did. For each of the four drugs in PEG 3350 the authors solved Eqs. 1 and 2 with $\Delta W_{d,p}=0$, using the properties in Table 1 (reproduced as Table A), and converted the crossing point to weight percent with Eq. 4. P6·M1·M5 The molecular weights, log P values and densities come from the Cambridge Structural Database (ref 48), the aqueous solubilities from the PhysProp database (ref 49), and the molar volumes were calculated as molecular weight over density; the paper does not say where the melting points and heats of fusion come from, although its Methods describe DSC measurements of the pure materials. M1·X10

Table A. Model inputs, transcribed from Table 1 of the paper. M1·M2·M3·M4·M5·M6

To see how a drug's melting point and its interaction with PEG trade off in general, the authors also ran the model for a hypothetical "average" crystalline drug with a molar volume of 250 cm³/mol, a heat of fusion of 35 kJ/mol and a molecular weight of 325 g/mol, at melting points from 80 to 350 °C and interaction energies of 0, −2.5, −5.0 and −10.0 kJ/mol (Figure 2). P7·A4

Contribution 2: measuring the real phase diagrams

What they did. The four drugs were chlorpropamide and haloperidol (Sigma-Aldrich), loratadine and aceclofenac (Attix Pharmachem), with PEG 3350 from Dow Chemical; their structures are in Figure 1. M1·M2·M3·M4·M5 Dispersions were made by the fusion method: 500 mg physical mixtures at a range of drug:polymer weight ratios were mixed geometrically, heated on a hot plate until melting began, cooled slowly to room temperature, ground and stored over phosphorus pentoxide (0% RH) for 24 h. The DSC series ran from pure PEG 3350 through 9:1 to 1:9 polymer:drug to pure drug; hot-stage microscopy added 5 wt% loratadine and 15 and 25 wt% haloperidol. P1·A2 DSC used hermetically sealed pans heated at 1 °C/min under nitrogen, with the offset temperatures of the eutectic and drug melting taken for the phase diagram; hot-stage microscopy heated 2–3 mg samples at 1 °C/min and recorded the temperature at which the last solid particle melted. P2·P3 How it differs. The two methods use different end points, and the paper plots both on the same diagram (Figure 4). R5·R6·R7·R8

Contribution 3: testing for interactions without the phase diagram

Problem. A back-calculated interaction energy only restates the gap between prediction and observation; it cannot show that an interaction causes the gap. What they did. First, excess crystalline drug was stirred in PEG 400 for 24 h at 25 °C, the liquid was centrifuged and filtered through a 0.45 µm PTFE filter, diluted in ethanol and assayed by UV against a five-point calibration ($R^2$ above 0.99); the activity coefficient followed from Eq. 7. P5·P9 Second, spectra of 25:75 drug–PEG 3350 mixtures were collected in the molten state by ATR-FTIR (40 mg samples, 500–4000 cm⁻¹, 4 cm⁻¹ resolution, 128 scans), at 130 °C for chlorpropamide, 160 °C for aceclofenac, 140 °C for loratadine and 155 °C for haloperidol, and compared with additive spectra of the pure molten components. P4 Why it works. If the drugs whose eutectic is underpredicted are also the ones that dissolve better than ideal and whose hydrogen-bonding bands move in molten PEG, the case that interactions cause the miss rests on more than one kind of evidence. C36

Experimental analysis

What the athermal model predicts

With no interaction term the model put the eutectic at 12.8 wt% drug for chlorpropamide, 6.5 wt% for loratadine, 1.5 wt% for aceclofenac and 0.5 wt% for haloperidol. R1 The authors read the haloperidol value as "indicative of a monotectic system", the aceclofenac value as low solubility, and the loratadine and chlorpropamide values as eutectic systems. C7 Under this assumption, they argue, the crystal lattice decides the prediction: haloperidol and aceclofenac melt at almost the same temperature (150.9 and 151.7 °C) but haloperidol's heat of fusion is higher (53.3 against 42.2 kJ/mol), which "explains" its lower prediction, and both have higher lattice energies than loratadine and chlorpropamide (135.3 and 126.7 °C; 27.9 and 24.5 kJ/mol). C9·M1·M2·M3·M4 They add that the drug's molecular weight and molar volume "play an insignificant role", as found earlier (ref 27); this paper does not test it. C8 On the phase diagrams, the predicted lines start at about 55 °C for pure PEG 3350, dip to minima of about 52.5–54.5 °C, and rise to each drug's melting point (read from Figure 4). R5·R6·R7·R8

Note by the AI writer (not discussed in the paper). Solving Eqs. 1, 2 and 4 with the Table 1 inputs reproduces three of the four predictions (aceclofenac 1.56, loratadine 6.36, haloperidol 0.56 wt%) and the Figure 2 series, but gives 9.45 wt% for chlorpropamide instead of 12.8 wt%; the chlorpropamide line in Figure 4a also lies below the Table 1 calculation (about 98 against 104.7 °C at 40 wt%). Some input for chlorpropamide must differ from Table 1; the paper does not say which. E1·X2

The model map: melting point against interaction

Figure 2 shows the same trade-off for the hypothetical drug. With no interaction, the predicted eutectic falls from about 19 wt% at a melting point of 80 °C to about 10 wt% at 100 °C and below 3 wt% from 150 °C on; each step toward more negative interaction energy lifts the whole curve (Table C). R2 The vertical lines the authors draw at about 100, 160 and 240 °C mark where the 0, −5.0 and −10.0 kJ/mol series cross 10 wt%. R3 In their words, as the melting point rises, the drug–PEG interactions "have to be" stronger to reach a 10% drug load. C11 They name four regions: below 100 °C, high eutectics even without interactions; 100–160 °C, appreciable loading only with significant interactions; 160–240 °C, very strong interactions needed; above 240 °C, the model "predicts that even very strong drug-polymer interactions are not enough", so minimal loading "would be expected". C12 All four real drugs fall in the second region. C19

Table C. Predicted eutectic composition (wt% drug) of the hypothetical drug in PEG 3350, read from Figure 2 (approximate). R2

The measured phase diagrams

The DSC traces (Figure 3) show the pattern the authors describe: two endotherms away from the eutectic and one near it. R4·C13 In every panel the PEG 3350 trace has a sharp endotherm at about 60.5 °C, and the pure drugs melt at about 128 (chlorpropamide), 152 (aceclofenac), 134.5 (loratadine) and 152 °C (haloperidol) (read from Figure 3). R4 The phase diagrams built from DSC and hot-stage microscopy (Figure 4) split the four drugs into two pairs (Table D). R5·R6·R7·R8

For haloperidol, PEG melting stayed near 59–61 °C and from 10 wt% the liquidus rose steeply toward the drug's melting point: a monotectic system with an observed eutectic below 1 wt%, "similar to that predicted from the model" (0.5 wt%). R8·R1·C14 For loratadine the liquidus stayed at about 58 °C at 5 wt% and rose from 10 wt%: an observed eutectic of approximately 5 wt% against 6.5 wt% predicted, which the authors call comparable. R7·R1·C14 Chlorpropamide and aceclofenac behaved very differently. The chlorpropamide liquidus stayed at about 55–60 °C from 10 to 40 wt% drug and climbed only from 50 wt%; at 40 wt% the model predicts about 98 °C. The aceclofenac liquidus stayed at about 55–60 °C from 10 to 30 wt%, and at 40 wt% it was about 86–88 °C against about 135.5 °C predicted (read from Figure 4). R5·R6 The observed eutectics were 35 and 30 wt%, against predictions of 12.8 and 1.5 wt%: a "significant disparity". R1·C15

Table D. Predicted and observed eutectic compositions (Table 2) and liquidus temperatures read from Figure 4 (approximate). R1·R5·R6·R7·R8

Note by the AI writer (not discussed in the paper). Three details of the measured diagrams deserve care. First, where the model "worked", the measured liquidus lies above the model line at intermediate compositions (loratadine by hot stage about 103 against 90.5 °C at 20 wt%; haloperidol about 137.5–146 against 119–133 °C at 15–30 wt%), so the agreement is in the eutectic composition, not in the whole curve. X6 Second, DSC and hot stage differ by up to about 16 °C for haloperidol at 20–25 wt% and by about 10 °C for loratadine at 10 wt%. X7 Third, the low-temperature endotherm, which the authors assign to eutectic melting, moves from about 58 °C in the 9:1 chlorpropamide trace to about 39–44 °C in the most drug-rich ones, and to about 47–49 °C in drug-rich aceclofenac traces, whereas a single eutectic should melt at one temperature; for loratadine and haloperidol it stays at about 56–61 °C. The paper does not comment. R4·X8 The observed eutectics were also located on a coarse grid: chlorpropamide's 35 wt% was not itself a tested composition. X9

Interaction energies and the Flory–Huggins parameter

Back-calculating the interaction energy from each observed eutectic gave values close to zero for haloperidol (−0.11 kJ/mol) and loratadine (0.34 kJ/mol), "indicative of minimal specific interactions", and negative values for chlorpropamide (−6.85 kJ/mol) and aceclofenac (−18.2 kJ/mol), aceclofenac "apparently" interacting most strongly because its miss was largest. R1·C16·C17 The negative values, the authors write, "imply" an additional driving force for these drugs to mix with molten PEG 3350 from a favourable enthalpy of mixing; both drugs melt in region II, where the athermal model predicts low eutectics. C18·C19 Converted with the model's eutectic temperature, the Flory–Huggins parameter was −2.53 for chlorpropamide, −6.68 for aceclofenac, 0.13 for loratadine and −0.04 for haloperidol, "indicating" athermal mixing for the last two and "signifying" exothermic mixing from specific interactions for the first two. R9·C27 Table B collects these values with the solubility results.

Table B. Eutectic compositions and interaction energies from Table 2; solubility in PEG 400 at 25 °C, mole fraction, activity coefficient and χ_dp from Table 3. R1·R9

Note by the AI writer (not discussed in the paper). The ${\chi }_{dp}$ values reproduce from the Table 2 energies with the model's eutectic temperature (for chlorpropamide, −6850/(8.314 × 326.13) = −2.53). E8 The Table 2 energies themselves do not reproduce: solving Eqs. 1 and 2 for $\Delta W_{d,p}$ with the Table 1 inputs gives −7.35, −14.5, +0.71 and −1.60 kJ/mol (chlorpropamide, aceclofenac, loratadine, haloperidol taken at 1 wt%) when the observed weight fraction is converted to volume fraction, or −8.97, −18.1, +0.31 and −2.0 kJ/mol when the weight fraction is used directly, against −6.85, −18.2, 0.34 and −0.11 kJ/mol printed. The signs and the order (aceclofenac most negative, then chlorpropamide, then the two near zero) hold in every variant; the exact values do not. X3

Solubility in PEG 400

Chlorpropamide (194 mg/mL) and aceclofenac (233 mg/mL) dissolved in PEG 400 above their ideal solubility, so their activity coefficients were well below 1 (0.614 and 0.121); assuming close to ideal entropy of mixing, the authors write, "this result suggests that favorable interactions can be formed between the drug and PEG". R9·C23 Loratadine (49 mg/mL, γ 2.369) and haloperidol (14 mg/mL, γ 0.842) were described as close to ideal, "supporting" the absence of specific interactions, their solubility being "largely dictated by the properties of the crystal". R9·C24 The authors conclude that solubility in PEG 400 is "predictive" of the PEG 3350 results and "might provide a useful screening tool" for drugs with higher than predicted eutectics. C25

Note by the AI writer (not discussed in the paper). The paper does not say how solubility in mg/mL was turned into $x_{\mathrm{d}\mathrm{r}\mathrm{u}\mathrm{g}}$. The printed values equal moles of drug per mole of PEG 400 in 1 mL of PEG 400 (for chlorpropamide, 0.194/276.7 divided by 1.12/400 = 0.250), a mole ratio; a true mole fraction would be 0.200, 0.190, 0.044 and 0.013, giving activity coefficients of 0.766, 0.149, 2.49 and 0.856. The split between the two groups survives either way. X4 Loratadine's γ of 2.369 means its measured solubility is about 0.42 of the ideal value, so "close to ideal" is generous; its positive ${\chi }_{dp}$ and $\Delta W_{d,p}$ point the same way. X13 The solubilities were measured at 25 °C, about 30 °C below the eutectic temperatures in molten PEG 3350, so they compare drugs rather than give values for the melt. X16

Infrared spectra of the melts

In the chlorpropamide melt the carbonyl band sat at 1717 cm⁻¹ against 1663 cm⁻¹ in the additive spectrum, and in the aceclofenac melt at 1744 against 1728 cm⁻¹ (Figure 5a, b). R10.a·R10.c The authors call these shifts "indicative of a change in drug-drug hydrogen bonding" because the drug now hydrogen bonds with PEG's hydroxyl or ether groups. C29 Since a PEG 3350 chain has 2 hydroxyl end groups but about 75 ether oxygens, they consider it "likely" that the drug donates its hydrogen bond to an ether oxygen, which leaves fewer drug donors for the drug's own carbonyls and moves those bands to higher wavenumber. R12·C30 For these two drugs, they write, the spectra "confirm that specific interactions do occur" and, with the solubility data, explain the model's failure. C31

Loratadine, which has only acceptor groups, showed its carbonyl band at the calculated position, with no evidence of hydrogen bonding of the carbonyl or tertiary nitrogen and no shift of the aromatic C–N band at 1322 cm⁻¹ (Figure 5c). R10.e·R10.f·C34 Haloperidol showed no carbonyl shift, which "may be due" to its tertiary nitrogen being the better acceptor; its aromatic C–N band at 1348 cm⁻¹ moved only nominally, and its OH stretching region matched the calculated spectrum (data not shown), "suggesting" no specific interactions (Figure 5d). R10.g·R10.h·R11·C32·C33 The spectra thus "appear to corroborate" the interaction parameters and solubility data for these two drugs. C35

Table E. Band positions in 25:75 drug–PEG 3350 melts: additive-spectrum values from the Figure 5 caption, measured values from the text, or read from Figure 5 (approximate) where marked "about". R10

Note by the AI writer (not discussed in the paper). In Figure 5c the second arrow sits at about 1345 cm⁻¹, the same position as the 1342 cm⁻¹ arrow in Figure 5a, not at the 1322 cm⁻¹ given for loratadine's C–N stretch. X11 More generally, the evidence is a shift of the drug's own carbonyl band against an additive spectrum; no PEG band (ether or hydroxyl) was analysed, so the bond to the ether oxygen remains an inference. X15

Discussion

The argument as a chain

The authors connect the results in a short chain. A drug's solubility in molten PEG depends mainly on two things: the crystal lattice energy, set by melting point and heat of fusion, and the strength of specific drug–polymer interactions compared with the interactions in the pure liquids; weak lattices or strong interactions "would be expected" to give high eutectic compositions. C10 The athermal model keeps only the first, so for drugs melting between 100 and 160 °C it predicts low loadings unless the drug interacts with PEG. C8·C12·C19 From there the four drugs split into two cases.

In the first case, the drug does not hydrogen bond to PEG, its activity coefficient in PEG 400 is near 1 or above, its back-calculated interaction energy is near zero, and the model is right. C33·C34·C24·C16·C14 In the second, the drug donates a hydrogen bond to PEG, "likely" to the ether oxygen, mixing becomes exothermic, the drug dissolves above ideal in PEG 400 (γ 0.614 and 0.121), and the eutectic sits at 30–35 wt% instead of 1.5–12.8 wt%. C30·C18·C23·C15·R9·R1 The authors' summary is that, "for the systems investigated", the accuracy of the model is delineated by the presence or absence of specific interactions, and that the prediction is "interdependent" on lattice energy and the nature of the drug–polymer interactions. C36·C37 The "good" and "bad" colours in the diagram refer to the model's accuracy, not to the formulation: the interacting drugs are the ones that can be loaded more heavily.

Where the model applies

The authors call the model "ideally suited" to drugs that lack specific interactions with the polymer, and they tie the influence of interactions to the drug's melting point. C38 The two statements of the melting-point condition disagree: the abstract restricts the model to compounds melting below 200 °C without drug–polymer interactions, while the conclusions recommend it for drugs with high melting temperatures (above 200 °C) or drugs lacking interactions. Neither value appears on Figure 2, whose region borders lie at about 100, 160 and 240 °C. X5·R3

Note by the AI writer (not discussed in the paper). Figure 2 is consistent with the conclusions' version. For a drug melting far above 200 °C the predicted eutectic is close to zero whatever the interaction, so the athermal prediction cannot be far off in absolute terms; for drugs melting around 100–160 °C, where all four real drugs lie, a moderate interaction can move the eutectic by tens of weight percent, so the athermal model is reliable there only if the drug does not interact. Which version the authors intended in the abstract cannot be settled from the paper. R2·R3·X5

What it suggests for formulation

The authors offer two practical tools. Solubility in PEG 400 "might provide a useful screening tool" for drugs whose eutectic in PEG exceeds the prediction, and with this understanding the usefulness of the model for a new chemical entity "can be quickly assessed" from its structure and physical properties. C25·C39 Both rest on the point the introduction makes: a eutectic dispersion is feasible only if the dose fits under the eutectic composition. C3

Note by the AI writer (not discussed in the paper). Read together, the results suggest a quick sequence for a crystalline PEG dispersion: estimate the athermal eutectic from melting point and heat of fusion (Figure 2 gives the scale: about 10 wt% at a melting point of 100 °C, under 3 wt% at 150 °C for an average drug); check the structure for a hydrogen-bond donor that can reach PEG's ether oxygens; for such a drug, measure solubility in PEG 400 and expect a higher eutectic if the activity coefficient is well below 1; then confirm with a DSC or hot-stage phase diagram. For the two donor drugs here the athermal prediction was a floor, 2.7 and 20 times below the observed eutectic. R2·R1·R9

What remains open

Several points are not settled by this paper. The proposed hydrogen bond to the ether oxygen was inferred from the drug's carbonyl band; no PEG band was analysed. C30·X15 All four drugs melt in region II, so the behaviour predicted for regions I, III and IV was not tested with real drugs. R3·C12 Experimental eutectic temperatures were not reported, and the downward drift of the low-temperature endotherm in the two interacting systems was not discussed. X8 The crystal forms of the drugs, as received and after fusion, were not characterised. X14

Limitations

Stated by the authors

The authors limit their main conclusion to "the systems investigated". C36 They note that PEG 400 "may have different chemistry" from PEG 3350 because of end-group effects, which may affect solubility, and that activity coefficients are hard to measure in high-molecular-weight, semicrystalline polymers, which is why the liquid analogue was used. C22·C21 They acknowledge that a molten mixture always shows some spectral differences from the additive spectrum because of non-specific interactions. C28 The claimed minor role of molecular weight and molar volume is taken from earlier work. C8

The AI writer's own judgement

Overall the paper's central result is moderately solid. The split between the two matching and the two missed drugs is large (factors of 2.7 and 20), well beyond the 5–10 wt% composition grid, and three independent readings (interaction energy, activity coefficient, carbonyl shift) agree on which drugs interact. R1·R9·R10 Against this:

• Only four drugs and one polymer were tested, all melting at 127–152 °C, so the general rule rests on the model map rather than on data. M1·M2·M3·M4·X5
• Eq. 3 as printed does not follow from Eqs. 1 and 2, and the Table 2 interaction energies cannot be reproduced from the printed inputs; only their signs and ranking are robust. X3
• The chlorpropamide prediction (12.8 wt%) recomputes to 9.45 wt% from Table 1, while the other three predictions reproduce. X2
• The conversion from mg/mL to mole fraction is not stated; the printed values behave like mole ratios. Loratadine (γ 2.369) is described as close to ideal. X4·X13
• The text assigns Eqs. 1 and 2 to the wrong sides of the eutectic, and the Table 3 caption cites the wrong equation numbers. X1·X12
• The model's PEG melting point (55 °C) is about 6 °C below the measured one (about 61 °C), and the source of the Table 1 melting data is not given. X10
• "Accurately predicted" refers to the eutectic composition only; DSC and hot stage differ by up to about 16 °C at some compositions. X6·X7
• The IR evidence is indirect, and the loratadine C–N band position in the text does not match the arrow in Figure 5c. X15·X11
• Activity coefficients at 25 °C in PEG 400 are compared with eutectics near 52–61 °C in molten PEG 3350. X16

Conclusion

Baird and Taylor tested whether a Flory–Huggins-based model, run with no drug–polymer interaction, can predict how much crystalline drug molten PEG 3350 holds at its eutectic. It did for haloperidol (0.5 predicted, below 1 wt% observed) and loratadine (6.5 against about 5 wt%), and failed badly for chlorpropamide (12.8 against 35 wt%) and aceclofenac (1.5 against 30 wt%). R1·C14·C15 The two failures were the drugs that dissolved better than ideal in PEG 400 and whose carbonyl bands moved in molten PEG, which the authors read as hydrogen bonds donated to PEG, "likely" to its ether oxygens. R9·R10·C30·C31 Model calculations add that the higher a drug melts, the stronger the interaction it needs to reach a useful loading. R2·C11·C12 The practical message is that the athermal prediction can be trusted for drugs that do not interact with PEG, and that a solubility measurement in PEG 400 "might provide" an early warning for those that do; the exact interaction energies, by contrast, should not be taken at face value. C38·C25·X3