One phase or two? Testing drug–polymer miscibility in amorphous solid dispersions with DSC, infrared spectroscopy and X-ray diffraction

Background and motivation

An amorphous drug dissolves to a higher apparent concentration than its crystal, which can raise absorption when dissolution limits it, but the benefit disappears if the drug crystallizes during manufacture or storage (refs 1–4) C1. Formulating the drug as an amorphous solid dispersion (ASD) with a polymer is one way to keep the amorphous form. Earlier studies showed that a polymer can significantly delay crystallization onset, and the effect has been attributed to lower molecular mobility, a lower thermodynamic driving force, a higher energy barrier to crystallization, disruption of the molecular recognition needed for crystallization, or several of these together (refs 5–12) C2.

The introduction stresses one condition that holds whatever the mechanism: the stabilizing effect is fully realized only when drug and polymer are "intimately mixed at the molecular level". Physical mixtures of indomethacin with PVP and of sucrose with PVP did not inhibit crystallization (Matsumoto and Zografi, ref 13; Shamblin and Zografi, ref 14) C3. A molecularly mixed binary system contains one amorphous phase; a system with more than one amorphous phase contains regions with different drug:polymer ratios, and these differences should show up in measured physical properties. Counting the amorphous phases therefore tells whether drug and polymer are mixed, and mapping the count against composition (or temperature) gives the limits of one-phase formation C4.

The usual tool for counting amorphous phases is differential scanning calorimetry (DSC): one glass transition temperature (Tg) is read as one phase and two Tgs as two phases, a criterion borrowed from polymer blends (refs 15–18) and called the "golden standard" C5. The authors list its known weaknesses. Domains smaller than about 15–30 nm may not give two distinct Tg events (refs 15, 20); the temperature rises during the scan, which can change miscibility while it is being measured; and a single Tg seen above the lowest component Tg says little about the phase state at room temperature C6·R25. Two other techniques offer a more local view. Infrared (IR) spectroscopy responds to the local chemical environment, so drug–polymer interactions such as hydrogen bonds change the spectrum; for felodipine–PVP and nifedipine–PVP, shifts of the drug NH band and a rise of the free drug carbonyl band with polymer content had already been reported and assigned to drug–polymer hydrogen bonding (refs 9, 10, 23, 26, 27) C7·C18·R23. Powder X-ray diffraction (PXRD), the least used of the three for this purpose, can be turned into a pair distribution function (PDF) that reflects nearest-neighbour distances, and Newman et al. had used it on indomethacin–PVP mixtures (refs 19, 20) C8.

For the systems studied here, DSC had already shown a single Tg between the component Tgs, varying with composition, for felodipine–PVP and nifedipine–PVP (refs 10, 23, 24); only selected data existed for ketoconazole–PVP (one Tg at 50% polymer and above, ref 6), and nothing for felodipine–poly(acrylic acid) (PAA) R5. The paper therefore sets out to characterize four binary systems, felodipine–PVP, nifedipine–PVP, ketoconazole–PVP and felodipine–PAA, at several drug-to-polymer ratios with all three techniques; to use principal component analysis (PCA) to make the reading of IR spectra less dependent on the operator; and to test whether PXRD, analysed by PDF fitting and by the Pure Curve Resolution Method (PCRM), can detect mixing C4·C12.

Background concepts

What "miscible" means: the free energy of mixing

The Discussion frames miscibility with the thermodynamics of liquid mixtures, which the authors extend to amorphous solids "in this work" C35. Mixing two components increases the combinatorial entropy. Assuming ideal mixing, the paper writes (Eq. 3):

In plain terms: the entropy gained on mixing depends only on the mole fractions $X_u$ and $X_v$ of the two components; $R$ is the gas constant. The text states that because each mole fraction lies between 0 and 1, $\Delta S_{mix}$ is always positive. As printed, however, the expression lacks its leading minus sign and would give a negative value (for example $-0.693R$ at $X_u=X_v=0.5$); the standard ideal-mixing form is $-R(X_u\ln X_u+X_v\ln X_v)$, which matches the sentence that follows E3·X7.

The enthalpy of mixing is defined as the difference between the enthalpies of the pure components and of the mixture (Eq. 4):

In plain terms: $H_{ii}$ and $H_{jj}$ stand for the pure components and $H_{ij}$ for the mixture, so $\Delta H_{mix}$ compares how strongly like molecules hold together with how strongly unlike molecules do. The authors note that it can be positive, negative or zero, and, in the convention of Eq. 4, call a positive value exothermic E4. Entropy and enthalpy combine in the Gibbs free energy of mixing (Eq. 5):

In plain terms: mixing is favourable when $\Delta G_{mix}$ is negative at the temperature $T$. Note by the AI writer (not discussed in the paper): Eq. 5 and the later statements in the Discussion, "if $\Delta H_{mix}$ value is negative, the two components will be completely miscible", use the usual convention in which $\Delta H_{mix}$ is the mixture minus the pure components, opposite to the definition in Eq. 4. Read with the usual convention, a negative (exothermic) enthalpy of mixing favours mixing X8.

Plotting $\Delta G_{mix}$ against composition gives three kinds of curve, sketched in Figure 12 (adapted from Rubinstein and Colby, ref 34). If $\Delta G_{mix}$ is negative with a single minimum, the two components are completely miscible. If it is positive, they do not mix and a completely phase-separated system forms; the authors add that strict immiscibility is rare, since some of one component always dissolves in the other, so a system is "immiscible from a practical point of view" when that amount is extremely small C36. In between lies partial miscibility: $\Delta G_{mix}$ is negative but has two minima. In the paper's words, these minima are the binodal points, which enclose a metastable region where separation proceeds by nucleation and growth and which can be found by setting the first derivative of $\Delta G_{mix}$ with respect to composition to zero; the inflection points between them, found by setting the second derivative to zero, are the spinodal points, which enclose an unstable region where separation is spontaneous E6·E7. Note by the AI writer: taking the binodal at the minima is exact only for a symmetric curve like the schematic in Figure 12; for an asymmetric drug–polymer system the coexisting compositions follow from the common-tangent construction X15.

The link to chemistry is the balance of interactions. If the drug–polymer interaction is "sufficiently favorable" compared with drug–drug and polymer–polymer interactions, $\Delta G_{mix}$ has one minimum and a one-phase dispersion is favoured; if the drug–polymer interaction is weak relative to the intra-species ones, more than one minimum appears and "the formation of more than one amorphous phase may be favored" C37.

DSC and the single-Tg criterion

A homogeneous amorphous blend shows one glass transition whose temperature lies between those of the components. To judge whether a measured Tg fits ideal mixing, the authors compare it with the Couchman–Karasz equation (Eq. 1, ref 25):

In plain terms: the expected Tg of the mixture, $T_{g,mix}$, is a weighted average of the component Tgs, $T_{g1}$ and $T_{g2}$, using the weight fractions $w_1$ and $w_2$; the second component is weighted by a constant $K$. The constant comes from the heat-capacity steps of the pure components at their glass transitions (Eq. 2):

In plain terms: the component whose heat capacity jumps more at its glass transition pulls the mixture Tg more strongly toward its own value. The paper does not print the $\Delta C_p$ values or $K$ E1·E2. Two Tgs, or one Tg far from this prediction, are taken as signs of incomplete or non-ideal mixing.

IR spectra and principal component analysis

If drug and polymer do not mix at the molecular level, as in a physical mixture of the two amorphous materials, the IR spectrum of any blend is simply the sum of the two pure spectra in proportion to composition. The authors therefore calculate "physical mixture" spectra from the measured spectra of pure amorphous drug and pure polymer and use them as the no-mixing reference (method of refs 26, 27) P4. Principal component analysis describes a set of spectra by a few directions of variation (principal components, PCs). Each spectrum receives a score on each PC (plotted as $t[1]$ and $t[2]$), and the loading of a PC shows which wavenumbers make it up. The authors' reasoning is as follows: in a set of physical mixtures, only composition changes, so one PC suffices and its loading resembles the difference between the two pure spectra; if drug and polymer interact specifically, for instance through hydrogen bonds, the chemical environment changes as well, and a second PC is needed whose loading shows these changes (PCA of physical mixtures had been applied before by Rantanen et al., ref 28) C9.

PXRD of amorphous solids: halos, pair distribution functions and pure curves

An amorphous solid gives no sharp Bragg peaks in PXRD, only broad humps called amorphous halos. Two analyses extract miscibility information from them. In the PDF fit, the diffraction pattern of each dispersion and of the pure amorphous drug and polymer is converted into a pair distribution function, which reports how often atom pairs occur at each distance; the pure-component PDFs are scaled and summed and the scale factors are varied until the sum best matches the dispersion PDF. If the two components sit in separate amorphous phases, the best fit reproduces the dispersion's peak positions and returns the true composition; if they are mixed, the dispersion has a PDF of its own, the sum cannot reproduce it and the fitted composition is off P8·C10. The Pure Curve Resolution Method instead uses the whole composition series: the variance across the patterns identifies how many independent components describe the set, and each is projected back into a "pure curve". For an immiscible system the two pure curves should look like the measured drug and polymer patterns, with no extra component; an extra component, or a halo shifted by about 1° 2θ or more, is taken as a structurally induced change and "interpreted as indirect proof of miscibility" P9·C11.

Methods in detail

The study has no new instrument or theory; its contribution is a comparison. Four drug–polymer pairs were chosen to span different kinds of interaction: felodipine and nifedipine with PVP, where drug–polymer hydrogen bonds were known from earlier work; ketoconazole with PVP, where, as the authors state, "no drug-polymer hydrogen bonds can be formed"; and felodipine with PAA, a polymer that forms many hydrogen bonds with itself (Dong et al., ref 33) A1·C22·R23·R24. Each pair was made at several drug:polymer ratios and examined by up to three techniques, each read against its own no-mixing reference A2·A4.

Materials and sample preparation

Felodipine was a gift from AstraZeneca; nifedipine and ketoconazole came from Hawkins, Inc.; PVP K29-32 and PAA (viscosity-average molecular weight Mv ∼450,000) from Sigma-Aldrich. Both polymers were dried over phosphorus pentoxide for at least a week M1–M5. Drug and polymer were dissolved together at the chosen weight ratio in a common solvent: a 1:1 w/w mixture of dichloromethane and ethanol for the PVP dispersions of felodipine and nifedipine, chloroform for ketoconazole–PVP, and pure ethanol for felodipine–PAA. Every solution was checked by eye to be clear and single-phase, the solvent was removed on a rotary evaporator in about 10 minutes or less, and the powders were kept under vacuum for at least 12 hours P1.

From this common starting point the three techniques used differently treated samples, a point that matters later. For DSC the powders were only ground gently P2. For IR, the solutions were spin-coated onto ZnS or KRS-5 windows, with the spin speed adjusted to give an absorbance between 0.4 and 1.0, and the films were dried for about a minute on a hot plate at 90 °C P3. For PXRD, the ground powders were heated in an aluminium pan to about 10 °C above the melting point of the drug for at least 15 minutes under dry nitrogen, quenched in ice and salt, and ground again into a coarse powder P6. The drug melting points are not given.

DSC protocols

DSC was run only on the two systems without published data, felodipine–PAA and ketoconazole–PVP, at 0, 10, 30, 50, 70, 90 and 100% polymer, in pinholed TZero pans on a TA Q2000 calibrated with indium and tin. Ketoconazole–PVP was heated from 0 °C to 180 °C at 20 °C/min. Felodipine–PAA was run in two regimens, "in case of heating-induced drug-polymer mixing": heating to 180 °C (Experiment 1 in Table I) or to 146 °C with a 30 s hold (Experiment 2). Each regimen was cycled two additional times, and midpoint Tgs are reported P2·A3. The paper does not say which cycle is shown, how much sample was used or whether any composition was repeated X10.

Contribution 1: reading IR spectra against calculated physical mixtures

The problem. Small shifts, shoulders and intensity changes in IR spectra of dispersions are the usual evidence of drug–polymer interaction, but judging them by eye is "sometimes subjective and can be affected by operator experience" C12. What they did. Spectra of the spin-coated films (500–4000 cm⁻¹, 4 cm⁻¹ resolution, 128 scans, dry-air purge) were collected for felodipine–PVP at 0, 10, 30, 50, 70, 90 and 100% PVP, nifedipine–PVP at 0, 25, 50, 70 and 100% PVP and felodipine–PAA at 0, 10, 30, 50, 70, 90 and 100% PAA; ketoconazole–PVP spectra are shown at 30 and 70% PVP. Physical-mixture spectra were calculated at 10–90% polymer from the pure-component spectra. Dispersions and calculated mixtures were analysed together by PCA in SIMCA-P+ over 700–4,000 cm⁻¹ after unit normalization P3·P4·P5. Why it works. Because the calculated mixtures by construction differ only in composition, they define a "composition-only" direction (PC1). A dispersion that needs a second direction to be described carries spectral changes that composition cannot explain, which the authors attribute to changed chemical environments from molecular-level mixing C9. How it differs from earlier work. Earlier studies of the same PVP systems identified hydrogen-bonding bands from the spectra themselves; here the same spectra are put on a common statistical scale against an explicit no-mixing reference.

Contribution 2: X-ray diffraction as a miscibility test

The problem. DSC fails when domains are small or when heating changes the phase state, and IR needs a spectroscopic handle such as a hydrogen bond. What they did. PXRD patterns of the melt-quenched powders were collected in transmission on a PANalytical X'Pert Pro with Cu Kα radiation, focusing optics, helium purge and an X'Celerator detector, after checking the instrument with a silicon standard (NIST SRM 640c), at 0, 30, 40, 60, 70 and 100% polymer for felodipine–PVP, ketoconazole–PVP and felodipine–PAA (Figures 8–10) P7. The PDF fit was applied at 30 and 70% polymer for all four systems (Table II) P8·R16; PCRM was applied to each composition series P9. Why it works. Both analyses ask whether the dispersion is fully described by its two pure components. A mixed phase has its own local packing and so its own PDF and halo positions; separate phases do not C10·C11. How it differs from earlier work. Newman et al. had applied the PDF approach to indomethacin–PVP (ref 20), and PCRM had been introduced by Ivanisevic et al. (ref 22); this paper applies both to systems whose miscibility is either well established (the PVP dispersions of felodipine and nifedipine) or uncertain, to test what they add to DSC and IR.

Experimental analysis

DSC: felodipine–PAA shows two Tgs at low PAA and unstable values at high PAA

Table A. Midpoint Tg of felodipine–PAA dispersions; two values = two glass transition events (from Table I) R1.

Pure amorphous felodipine had a Tg of 48 °C and PAA one of 132 °C in both regimens. At 10 and 30% PAA (90 and 70% felodipine) both regimens showed two Tgs, one at the felodipine value (46–48 °C) and one at or just above the PAA value (130–133 °C), where a single mixed phase would be expected at 59 and 79 °C. The weakest of these second transitions had a heat-capacity step of only 0.044 J/g°C, which the authors consider reasonable for the small amount of polymer R1·R2·C14. At 50% PAA, Experiment 1 gave two Tgs (48 and 121 °C) and Experiment 2 one (102 °C, prediction 96 °C). At 70 and 90% PAA one Tg was seen, but it moved by 30–35 °C between regimens (121 versus 86 °C; 114 versus 84 °C) and did not follow the prediction of 112 and 126 °C R1.

The authors conclude that "felodipine and PAA are at least partially immiscible", based on the two Tgs at 70 and 90% felodipine ("These results suggest"), and that the variability in the other samples "could be an indication of temperature-dependent mixing and/or miscibility" C13·C15. As an internal check, a single value $K\approx 1.33$ (felodipine as component 1) reproduces every Couchman–Karasz prediction in the table within rounding (58.8, 78.5, 111.6 and 125.5 °C against the printed 59, 79, 112 and 126 °C), so the predicted column is consistent with one set of $\Delta C_p$ values, even though these are not printed E1.

DSC: ketoconazole–PVP shows one Tg everywhere

Table B. Ketoconazole–PVP Tg against the Couchman–Karasz curve (read from Figure 2, approximate) R4.

Each thermogram in Figure 1 shows one glass transition, rising from about 50 °C without PVP to about 165 °C for pure PVP, with no second event marked up to about 175 °C; the pure ketoconazole trace has a small endothermic overshoot at its transition R3. The authors describe the measured values as "in reasonable agreement" with Couchman–Karasz, note that this matches the earlier report of one Tg at 50% PVP and above, and conclude that the results "suggest molecular level mixing" C17·R5. Read from Figure 2, the points fall about 7–10 °C below the curve at 10 and 30% PVP, lie a few degrees above it at 50 and 70%, and the 10% PVP value (about 44 °C) lies slightly below that of pure ketoconazole (about 47 °C) X9. In the Discussion the authors themselves qualify the DSC result: "it is possible" that a single phase forms only because the sample is heated, or that more than one phase exists but is "not well-detected" by DSC C42.

IR: felodipine–PVP and nifedipine–PVP dispersions differ from physical mixtures

In the felodipine–PVP score plot (Figure 3a) the calculated physical mixtures, from 10% PVP on the right to 90% PVP on the left, lie on a nearly flat line ($t[2]$ between about −0.5 and −0.15): one PC describes them. The dispersions sit clearly above that line, at $t[2]$ of about 0.8, 0.6, 1.25 and 1.2 for 10, 30, 50 and 70% PVP; the 90% PVP dispersion is only slightly above it (about 0.15), and the two pure components lie on it. The PC1 loading has the same features as the spectrum of PVP subtracted from that of amorphous felodipine, so PC1 carries composition; the PC2 loading is largest in the NH region (boxed in Figure 3b) and the carbonyl region R6·R7. Nifedipine–PVP gives the same picture (Figure 4): calculated mixtures at $t[2]$ of about −0.75 to −0.2, dispersions with 25, 50 and 70% PVP at about 1.6, 2.1 and 1.3 R8·R9.

The authors state that it is "obvious" that PC1 alone describes the calculated mixtures, that the dispersion scores are "well-separated" from them, that the PC2 loading "is thought to arise" from drug–polymer interactions, with the NH and carbonyl features "presumably reflecting" drug–polymer hydrogen bonds, and conclude that visual inspection and PCA together "suggest complete drug-polymer miscibility for both systems" C19·C20·C21.

IR: ketoconazole–PVP changes little, felodipine–PAA looks like a physical mixture

Ketoconazole–PVP was harder. Ketoconazole cannot hydrogen-bond to PVP, and its carbonyl-region spectra (Figure 5) kept every peak at the pure-component wavenumber; the only difference from the calculated mixtures was a slightly lower ketoconazole carbonyl peak, seen in all dispersions and shown at 30 and 70% PVP C22·R10. Recalling a report of ion–dipole interactions between PVP and another compound (ref 29), the authors write "It is speculated" that dipole–dipole interactions cause the change. They conclude that at least some molecules experience a different environment from mixing, but that the extent of miscibility cannot be judged from such limited changes C23·C24. PCA was abandoned for this system because the calculated physical mixtures, which should need only one PC, already needed two, for a reason that "could not be elucidated" R11·C25.

For felodipine–PAA, most dispersion spectra resembled the calculated mixtures by eye in both the carbonyl and NH regions (Figure 6) R12. In the PCA, the calculated mixtures needed one PC and the dispersions three; the PC1 loadings of the two sets correlated with a Pearson coefficient above 0.99, so PC1 again describes composition. The dispersions at 30, 50 and 70% PAA lay close to the mixture line ($t[2]$ between about −0.3 and 0.0). The 10 and 90% PAA dispersions were outliers: the 90% PAA sample could only be described by including PC2 ($t[2]$ about 3.2) and the 10% PAA sample varied along PC3 R13·R14. The authors read the 30–70% PAA samples as showing "a low extent of miscibility" that "resemble a physical mixture", and the two outliers as "suggesting that there may be some level of molecular level mixing" C26·C27. Note by the AI writer: the two outliers are also displaced along PC1, the composition axis (about −2.35 for 10% PAA, among the 80–90% PAA mixtures, and about 1.7 for 90% PAA, near the 30% mixture), and the paper reports no check of their composition X13.

PXRD: what the PDF fit returns

All PXRD patterns, from 0 to 100% polymer, showed only amorphous halos, so every sample was X-ray amorphous R15·C28. Table C lists the PDF fits.

Table C. Actual versus PDF-calculated polymer concentration (from Table II) R16.

The authors report "poor agreement" for every system except felodipine–PAA and one ketoconazole–PVP sample, and conclude that this indicates "at least partial miscibility" for the three PVP systems and "limited miscibility" for felodipine–PAA within the concentrations studied C29. They add that a good composition match "may indicate limited miscibility" but should be backed by looking at the PDFs themselves C30. Figure 11 does this for felodipine. For the 70% polymer samples the contrast is clear: the felodipine–PAA dispersion PDF and the calculated one nearly coincide (maxima at about 4.7 and 8.2 Å, minimum at about 6.6 Å), whereas for felodipine–PVP the dispersion curve is lower at the first and second maxima (about 10 versus 15 and 26 versus 34) and lacks the calculated minimum near 11.7 Å and maximum near 14 Å. For the 30% polymer samples the felodipine–PVP pair agree in peak positions (maxima at about 4.5 and 9.1 Å), while the felodipine–PAA dispersion shows a maximum at about 7.9 Å where the calculated curve is close to zero R17·R18. The authors summarize Figure 11 as "confirming limited miscibility" for felodipine–PAA and "larger differences" for felodipine–PVP C31.

Two problems in this part of the paper deserve attention. First, the text names the agreeing ketoconazole sample as the one "containing 70% drug", but Table II, whose column is polymer concentration, shows the good fit at 70% polymer (69) and a large miss at 30% polymer (15). The Discussion then states that "significant molecular level changes were observed for samples containing 70% PVP, but not for samples containing 30% PVP", which agrees with the text but, under the paper's own PDF criterion, not with the table. Either the ketoconazole rows of Table II are given as drug content or the text is wrong; the paper does not allow us to decide X1. Second, no threshold for "good" agreement is stated: felodipine–PVP at 30% (37, a 7-point gap) counts as poor, felodipine–PAA at 70% (64, a 6-point gap) as good X14.

PXRD: pure curves

Table D. Halo positions of measured pure components and PCRM pure curves (read from Figures 8b, 9b and 10b, approximate) R19·R21·R22.

In felodipine–PVP the felodipine pure curve keeps its first halo at about 11.5° but moves its second halo by more than 1° 2θ toward lower angle, and the PVP curve moves less. The authors read these shifts as "indicative of structural changes taking place as a result of mixing", an "indirect sign of miscibility", and report the same for nifedipine–PVP without showing the data R19·R20·C32. In felodipine–PAA the pure curves reproduce the measured felodipine and PAA patterns, so the system "is thought to be immiscible over the range studied (30–70% drug concentrations)" R22·C33. Ketoconazole–PVP is in between: a slight shift of the PVP halos and a broader ketoconazole halo "could be indicative of minor structural changes", which the authors take as "confirming the hypothesis" that the system is at least partially miscible R21·C34. Note by the AI writer: read from Figure 9b, the first PVP halo moves by about 1.2°, close to the 1° that the method treats as a significant shift, although the text calls it below 1° X11.

The three methods side by side

Table E. Summary of the evidence for each system (compiled from Tables I and II and Figures 1–11) R1·R4·R5·R6·R8·R10·R13·R16·R19–R22·C38·C40·C44.

Discussion

The authors connect the three systems through the balance of interactions in the free energy of mixing. Their chain of reasoning can be drawn as follows.

For felodipine–PVP and nifedipine–PVP, drug–polymer hydrogen bonding "in addition to entropic effects" is said to be "favorable to the mixing", giving one-phase dispersions; the authors call the agreement of the three methods for these systems "good" and say it "clearly established" one-phase mixtures "over the range of compositions studied" C38·C39. For felodipine–PAA they note that hydrogen bonding between drug and polymer is possible, but "it is speculated that the lack of complete miscibility is caused by competition with intra-species interactions", because PAA forms multiple hydrogen bonds with itself, which "would decrease the value of $\Delta H_{mix}$" in the sign convention of Eq. 4. The 30–70% PAA samples are pictured as a drug-rich and a polymer-rich phase, "each contain[ing] only a small fraction of the second component" C44·C45. At 10 and 90% PAA, where IR hinted at some mixing, they speculate that some mixing occurred while an excess of one component remained as its own phase. Here the Discussion cites "more than one Tg for samples containing 90% PAA"; Table I instead shows two Tgs at 10% PAA (90% felodipine) and one at 90% PAA, so the statement most likely refers to 90% felodipine C46·X2.

Ketoconazole–PVP does not fit either branch cleanly. No hydrogen bond is possible, IR changes are slight, and the authors read the PXRD result as structural change at 70% but not at 30% PVP, which "seemed to suggest a partially miscible system, where significant drug-polymer mixing indicative of a single amorphous phase occurs only at higher levels of PVP" C40. They point out that IR is a weak probe here, since "partial mixing may still result in the enhancement of certain spectral features", and that DSC's single Tg may reflect heating-driven mixing or poor detection; their own conclusion is that "This system clearly needs further investigation" as a function of composition and temperature C41·C42·C43.

The general conclusion is methodological. DSC, IR and PXRD "provide complementary results"; IR with PCA "can be utilized to verify drug-polymer mixing at the molecular level"; PXRD with PDF and PCRM "may be able to verify drug-polymer mixing for both completely and partially miscible systems"; and both are "especially useful" when DSC is "inconclusive or variable" C47·C48. Note by the AI writer (not discussed in the paper): for formulation work, the most useful lesson may be the felodipine pair. The same drug mixes with PVP, which accepts its NH hydrogen bond, but not with PAA, which prefers to hydrogen-bond to itself. Whether a polymer can interact with a drug is therefore not enough; what counts is whether the drug–polymer contact wins over the polymer's and the drug's own interactions. The paper does not measure these interaction strengths, so this remains the authors' interpretation, supported by earlier spectroscopic work rather than by new data C39·C45.

Limitations

Limits the authors state

The authors list the weaknesses of DSC themselves: domains below 15–30 nm may give one Tg, the scan can change miscibility, and a single Tg above the lowest component Tg says little about room temperature C6. They state that visual reading of IR spectra is subjective, that the extent of ketoconazole–PVP miscibility cannot be judged from its very limited spectral changes, that PCA failed for that system for an unexplained reason, and that a good PDF composition fit should be supported by visual examination of the PDFs C12·C24·C25·C30. They call ketoconazole–PVP "challenging to fully characterize" and in need of further work C41·C43.

The AI writer's own judgement

(1) The ketoconazole–PVP conclusion rests on a contradiction. The claim that ketoconazole–PVP is one-phase only at high PVP comes from the PXRD composition fit, but the text and Table II assign the good fit to opposite compositions (see above). Read literally with the paper's own criterion, Table II would point to mixing at 30% PVP and separate phases at 70%. Until this is resolved, the composition dependence of ketoconazole–PVP miscibility should be treated as open X1.

(2) The three methods did not see the same samples. DSC used ground powders, IR used spin-coated films dried for a minute at 90 °C, and PXRD used powders that had been held about 10 °C above the drug melting point for at least 15 minutes and then quenched. The authors themselves raise temperature-dependent mixing for felodipine–PAA and heating-driven mixing for ketoconazole–PVP, so differences between the methods may reflect sample history as much as method sensitivity. The PXRD results describe melt-quenched material, not the solvent-evaporated dispersions X4.

(3) The criteria are qualitative and the samples single. No threshold separates a good from a poor PDF fit (6 versus 7 percentage points decide the cases), the PCA settings and the rule for the number of components are not given, and each DSC value is a single determination of an unstated heating cycle X14·X12·X10. The DSC evidence for felodipine–PAA immiscibility covers 10–30% PAA (and 50% in one regimen), not the 30–70% range stated in the abstract, which rests on IR and PXRD X3. "Complete range of concentration" for the PVP dispersions of felodipine and nifedipine means 10–90% and 25–70% PVP in the data shown, with the nifedipine PXRD results not shown and the DSC of both taken from earlier work X5.

(4) Small inconsistencies in the theory section. Eq. 3 is printed without its minus sign, and the sign convention for $\Delta H_{mix}$ changes between Eq. 4 and the rest of the Discussion. Neither affects the experimental conclusions, but a reader who uses these equations should take the standard forms X7·X8.

Taken together, the contrast between the PVP dispersions of felodipine and nifedipine on one side and felodipine–PAA on the other is consistent across IR and PXRD and is the paper's most solid result; the ketoconazole–PVP and the 10 and 90% PAA conclusions are tentative.

Conclusion

This paper tested whether two structure-sensitive methods, IR spectroscopy read through principal component analysis against calculated physical mixtures, and PXRD read through pair-distribution-function fits and pure-curve resolution, can establish drug–polymer miscibility where DSC is unclear. For felodipine–PVP and nifedipine–PVP both methods detect mixing at every intermediate composition tested; for felodipine–PAA both detect two separate phases between 30 and 70% PAA, in line with the two Tgs DSC finds at low PAA. For ketoconazole–PVP, where DSC gave a single Tg at every ratio, IR changed little and PXRD pointed to partial miscibility, but with a composition assignment the paper itself contradicts. The authors conclude that the three techniques are complementary and that IR and PXRD are "especially useful" when DSC is inconclusive or variable; the mechanism they propose, drug–polymer hydrogen bonding against polymer self-association, is taken from earlier work and was not measured here.