Finding trace crystals in amorphous drug–polymer powders with second harmonic generation imaging

Background and motivation

Amorphous solids are "increasingly under investigation" as a way to raise the apparent solubility, dissolution rate and potential bioavailability of poorly soluble drugs (Hancock 1997; Shan 2008). Their development is held back by their tendency to crystallize and by the lack of tools that detect low levels of crystallinity (Hancock 2002). Trace crystals matter more than their mass suggests: the authors cite work showing that even low levels of crystals can act as nucleation centres that accelerate crystallization during storage and dissolution, and so cancel the advantage of the amorphous form (Rodriguez-Hornedo 1999; Fletcher 1963; Vekilov 2010). The usual formulation answer, a polymeric crystallization inhibitor in a solid dispersion, creates its own measurement problem. The polymer dilutes the drug, leaving little crystallizing material per unit volume, and it can interfere with the analytical technique.

The standard toolbox includes differential scanning calorimetry (DSC), powder X-ray diffraction (PXRD), microscopy, Raman and infrared spectroscopy, and solid-state NMR (ssNMR), usually used together (Byrn 1999; Taylor and Zografi 1998; refs 15–17). Most of these cannot detect crystallinity below about 1%. ssNMR is sensitive, but a measurement can take hours, during which crystallinity may change; DSC heats the sample and can change it during the run. Transmission and scanning electron microscopy (TEM, SEM) need sample preparation, TEM is hard to use on powders, and both probe small fields of view that can miss rare crystals. The authors therefore look for a method that is quick, needs little sample preparation, and gives both a microscopic picture and a macroscopic number for powders.

Second harmonic generation (SHG) is their candidate: intense laser light interacting with a material that lacks inversion symmetry produces light at twice the energy. Rades and coworkers used SHG to quantify polymorphs with a calculated limit of detection below 5%, and to quantify crystallinity in mixtures of polyvinylpyrrolidone (PVP) with enalapril maleate and with ranitidine hydrochloride (Strachan 2004; Strachan 2005; Rawle 2006). The Purdue group built a laser-scanning SHG microscope for this purpose, SONICC (second-order nonlinear optical imaging of chiral crystals). With it they detected crystallites of 90 nm in an optically transparent medium (Wanapun 2010), and in cryomilled griseofulvin powder they followed the loss of crystallinity in agreement with PXRD while detecting crystals down to 0.04% (Wanapun 2011).

Two gaps remained. SONICC had not been applied to solid dispersions, and, "most significantly" in the authors' words, the scaling of SHG with crystallinity had not been established there. Earlier evidence in pure powders "suggests" linear scaling, but it rested on PXRD comparisons at a few crystallinity values. Linear scaling is not the obvious expectation: in thin ordered films and pristine single crystals SHG scales quadratically, so linear scaling would imply incoherent addition of SHG within microcrystals. Earlier measurements also used unfocused or gently focused light, and "it is not clear" that linearity holds when the focal volume (about 1 µm) is of the order of the crystal size. The point is practical: with a curved response, normalising a sample to a single crystalline standard would give wrong numbers.

The paper therefore uses SONICC to detect and quantify SHG from microcrystals in physical mixtures of naproxen and hydroxypropyl methylcellulose acetate succinate (HPMCAS), and in a naproxen–HPMCAS solid dispersion. PXRD and Raman serve as reference methods "with known linear scaling". The comparison is meant to show how SHG scales with crystallinity and how low a crystalline content it can detect when most of the powder is polymer. One drug, one polymer and one dispersion composition keep the comparison clean, and also set the limits of what can be generalised.

Background concepts

Linear and nonlinear polarization. The electric field of light induces a polarization in a material, which then acts as the source of a secondary wave. In ordinary optics the polarization is proportional to the field (Eq. 1):

Here $P^{(1)}$ is the first-order induced polarization, ${\chi }^{(1)}$ the linear susceptibility, $E$ the applied electric field and $\omega$ the frequency of the light. In plain terms: weak light makes the material respond at the same frequency and in proportion to the field. Under an intense field, such as a focused femtosecond laser, and in the limit of weak intermolecular interactions, the polarization becomes a power series (Eq. 2):

In plain terms: the response has parts proportional to the field, to its square, to its cube and so on, and the higher parts matter only when the field is very strong. The second-order term mixes two input waves into a new frequency (Eq. 3):

Here ${\chi }^{(2)}$ is the second-order susceptibility tensor and ${\omega }_{\mathrm{s}\mathrm{u}\mathrm{m}}={\omega }_1+{\omega }_2$. In plain terms: two photons combine in the material into one photon at the sum frequency. SHG is the case ${\omega }_1={\omega }_2=\omega$, giving light at $2\omega$; here the laser is at 800 nm and the SHG is collected at 400 nm.

Why amorphous material is silent. The bulk susceptibility is an orientational average of the molecular response (Eq. 4, read as a proportionality):

Here $I$, $J$, $K$ are laboratory axes, $i$, $j$, $k$ molecular axes, $N$ the number density, $R$ the rotation matrix between the frames, the angle brackets an average over orientations, and ${\beta }_{ijk}$ the molecular hyperpolarizability element. In plain terms: each molecule's response is projected onto the laboratory axes according to its orientation and summed; if all orientations are equally likely, the projections cancel. The printed equation shows "α" where a proportionality is meant, $N_0$ where the text defines $N$, and a garbled first rotation factor, and the text calls $\beta$ the "number element" (card note X2), so it is best read qualitatively.

From this follows the selection rule on which the method rests. SHG arises only where inversion symmetry is missing: at surfaces and in the majority of space groups of chiral crystals. Because the net signal is a coherent sum over all molecules, "amorphous materials, liquids, solutions, and centrosymmetric crystals do not generate a net coherent SHG signal". In a drug–polymer powder, the amorphous polymer and amorphous drug therefore add almost no background, and SHG-active crystals stand out on a dark field. The same rule limits the method: a drug that crystallizes in a centrosymmetric space group, routine for achiral compounds, is invisible. Note by the AI writer (not discussed in the paper): naproxen is used as a single enantiomer, which is why its crystals can be SHG-active; the paper does not print its crystal form or space group.

Coherent and incoherent addition. Whether SHG grows linearly with the amount of crystal depends on whether waves from different regions add in phase. For two sources $a$ and $b$ that are in phase, the fields add before squaring (Eq. 5); with random phases, the intensities add (Eq. 6):

Here $I^{2\omega }$ is the SHG intensity, the subscripts $c$ and $i$ denote the coherent and incoherent cases, and $E_a^{2\omega }$ is the SHG field from source $a$. In plain terms: in-phase sources reinforce each other, so the coherent signal rises with the square of the number density of sources, while sources with random phases simply add their brightness, so the signal rises linearly. The printed equations show source $a$ twice although the text describes sources $a$ and $b$; the second term is read here as $b$ (card note X1).

For SHG collected backward (epi-detected), the coherence length along the beam is about 100 nm (Wanapun 2010). A pristine crystal thicker than this gains nothing from added thickness; its intensity oscillates with thickness, and because it still rises with the square of the cross-sectional area, the authors expect overall scaling with volume to the power 4/3 ($V^{4/3}$). Lattice imperfections over more than 100 nm, or polycrystallinity, break the coherence, each domain becomes an independent source, and scaling becomes linear. Scaling therefore "may depend sensitively on the nature of the crystals formed", which is why it must be measured.

Chemometric terms. PXRD and Raman crystallinity were read from whole patterns or spectra by orthogonal projections to latent structures (OPLS), a multivariate regression on calibration samples of known crystallinity. Data were mean-centred, and Raman spectra were also corrected by standard normal variate (SNV) scaling, which removes overall intensity fluctuations, and log-transformed. Model quality is given as $R^2$, $Q^2$ (its cross-validated equivalent) and the root mean square error of estimation (RMSEE). RMSEE is the fit error on the calibration samples themselves; the independent prediction set, three compositions left out of calibration, is the real test. The 95% prediction bands show where a new measurement is expected to fall.

Two crystallinity bases. For the physical mixtures, "% crystallinity" is the weight percentage of crystalline naproxen in the whole powder. For the dispersion, it is the fraction of the drug that is crystalline: the dispersion is 25 wt% naproxen, and its SHG is normalised to a 75 wt% HPMCAS–25 wt% crystalline naproxen mixture (card note X11). A dispersion reading of 24% therefore means about 6 wt% crystalline naproxen in the powder (card note X9).

Methods in detail

The work splits into three contributions. The first calibrates SONICC on weighed physical mixtures of crystalline naproxen and HPMCAS, side by side with PXRD and Raman models built on the same samples, which tests linear scaling and accuracy. The second asks how little crystal SONICC can see in a powder that is almost all polymer, by three-dimensional imaging at 0.1% and a calculated detection limit. The third applies the method to a real solid dispersion: the fresh material, a spike-recovery test, and a 48 h crystallization study at 60 °C followed by all three techniques.

Contribution 1: Calibrating SONICC on physical mixtures against PXRD and Raman

① Problem. To turn an SHG image into a crystallinity number, the integrated signal must rise in a known way with the amount of crystal. Theory allows anything between linear and quadratic, and earlier powder evidence came from a few points measured with loosely focused light. A calibration under SONICC's tightly focused imaging conditions, with a polymer present and against independent reference methods, was missing.

② What they did. Crystalline naproxen free base (Sigma–Aldrich) and HPMCAS (Shin-Etsu AQOAT, type AS-MF) were weighed and milled together in a SPEX SamplePrep 6750 freezer mill at 8 Hz, after 5 min equilibration at liquid-nitrogen temperature, in cycles of 2 min milling and 1 min cooling (number of cycles not printed). The powders were warmed to ambient, handled in a dry-nitrogen glove box and sieved to below 105 µm. Compositions ran from 0 to 100% crystalline naproxen in triplicate; read from Figure 3, the levels were several below 2%, then 2, 5, 7.5, 15, 25, 35, 50, 65, 75, 90 and 100%. An independent prediction set at 3.5, 18 and 83% was milled the same way.

The SONICC instrument (Figure 1) used a Spectra-Physics Mai Tai laser (800 nm, 100 fs, 80 MHz) at 20 mW average power through a 10× objective of 0.3 numerical aperture, with a resonant mirror (about 8 kHz) and a galvanometer for scanning. One frame with 1000 averages per line took 25 s; the focus was stepped by 20 µm, and the resolution was 4 × 4 × 20 µm³. SHG at 400 nm was isolated by band-pass filters and counted by photomultipliers. About 1–2 mg of powder was held between slide and cover glass with 150 µm spacers, three fields of view were imaged per sample, and backward (epi) SHG was used for quantification. The 20 mW power was chosen "to ensure a linear dynamic range". Relative crystallinity was computed as follows (stated in words in the paper; card relation E8):

Here ${\overline{I}}_{\mathrm{s}\mathrm{a}\mathrm{m}\mathrm{p}\mathrm{l}\mathrm{e}}$ is the average SHG intensity integrated over the field of view, ${\overline{I}}_{\mathrm{H}\mathrm{P}\mathrm{M}\mathrm{C}\mathrm{A}\mathrm{S}}$ the "near-zero" average background of pure HPMCAS (value not printed), and ${\overline{I}}_{\mathrm{r}\mathrm{e}\mathrm{f}}$ the same quantity for the reference: 100% crystalline naproxen for the blends, or a 75 wt% HPMCAS–25 wt% crystalline naproxen physical mixture for the dispersion. In plain terms: the measured brightness, minus what the polymer alone gives, is expressed as a percentage of the brightness of a fully crystalline standard. This one-point normalisation is valid only if the response is linear and the crystals in the sample resemble those in the standard.

PXRD used a Shimadzu XRD-6000 with Cu-Kα radiation at 40 kV (current printed as "30 mV", presumably mA; card note X7), 5–35° 2θ at 4°/min with a 0.04° step, and a silicon external standard. Raman used a Kaiser RamanRxn1 at 785 nm with a non-contact probe, averaging 6–10 regions of the powder bed, in triplicate. OPLS models were built in SIMCA P+ 12: full-pattern for PXRD, and 3120–500 cm⁻¹ with SNV correction and log transformation for Raman.

③ Why it works. SHG is tested against two methods believed to respond linearly, on the very same powders, so composition errors affect all three alike. HPMCAS adds almost no SHG, so the zero point of the calibration is well defined. The low numerical aperture and large field of view average over many particles, and three fields of view per sample add further averaging. The prediction set checks whether the fitted line predicts compositions it has not seen.

④ How it differs from earlier work. Earlier evidence for linear scaling in powders came from a few PXRD comparisons with loosely focused light (Wanapun 2010). Here the calibration spans 0–100% in triplicate with a separate 0–25% check, uses tightly focused imaging, includes a polymer diluent, and is benchmarked against two independent techniques. Compared with the ensemble SHG measurements of Rades and coworkers, SONICC also locates individual crystals in an image.

Contribution 2: Imaging crystals at 0.1% and estimating a detection limit

① Problem. A linear calibration over 0–100% says little about the lowest levels. For an amorphous formulation the question is whether a few crystals in a large mass of polymer can be seen at all, or whether the polymer hides them.

② What they did. The authors recorded three-dimensional z-stacks of pure crystalline naproxen and of 0.1% crystalline naproxen in 99.9% HPMCAS (Figure 4), 3 min per 3D image; frame times can range from 10 s (about 200 averages per line) to several minutes. For one crystallite they plotted SHG intensity against scanned depth. They then estimated a detection limit from the single-voxel signal (card relation E9):

Here $S_3$ is the signal in one voxel (4 × 4 × 20 µm³) that would give a signal-to-background ratio of 3 within the volume probed for a sample containing no naproxen, and $S_{100}$ is the signal of the 100% crystalline powder. In plain terms: the smallest signal distinguishable from the polymer background in one voxel is expressed as a fraction of the signal of pure crystals. Single-voxel intensities "can have a broad distribution" because crystal size and orientation vary, so this is a mean limit. The intensities used and the background value are not printed (card note X10).

③ Why it works. Because the polymer gives almost no SHG, the background per voxel is very low, and a single crystal concentrates its signal in one or a few voxels. An ensemble method sees 0.1% crystal as a 0.1% contribution to a pattern dominated by the amorphous halo; an imaging method sees it as a bright point on a dark field. The depth profile confirms that the spot is a localised object.

④ How it differs from earlier work. Rades and coworkers reported an ensemble-averaged detection limit of 0.12% (1.2 parts per thousand) for PVP–enalapril maleate form II mixtures (Strachan 2004); the authors credit femtosecond lasers and optimised imaging for the improvement (Kissick 2011). Against amorphous griseofulvin films, where SONICC reached the order of parts per trillion (Wanapun 2010), the limit here is higher "because of the nonzero background from the polymer".

Contribution 3: Applying SONICC to a solid dispersion

① Problem. In a dispersion, crystals form in a polymer-rich matrix and the reference methods become harder to calibrate. Accurate PXRD quantification in dispersions "often requires" standards made from the amorphous dispersion plus crystalline drug, because the dispersion halo is "not necessarily the sum" of the pure amorphous halos (Rumondor and Taylor 2010; Rumondor 2009). Raman spectra of dispersions are "generally not simple" to interpret, so chemometrics are needed. Can SONICC follow early crystallization in such a matrix with a simpler calibration?

② What they did. A dispersion of 75 wt% HPMCAS and 25 wt% naproxen was made by rotary evaporation from dichloromethane–ethanol (1:1 by weight), dried under vacuum overnight, cryomilled and sieved to below 105 µm. It was stored at 60 °C and sampled at 0, 1, 2, 4, 6, 8, 12, 24 and 48 h (read from Figure 7) for SONICC, PXRD and Raman; the storage relative humidity and container are not printed (card note X13). For PXRD and Raman, standards were made by cryomilling crystalline naproxen with the dispersion to give 75/25 blends with different crystalline-to-amorphous naproxen ratios (levels not printed). For SONICC, the signal was instead normalised to a 75/25 physical mixture with crystalline naproxen. Finally, a partially crystallized dispersion was spiked with a known amount of crystalline naproxen and measured by SONICC; the amount added and the sample's history are not printed.

③ Why it works. If the response is linear and the amorphous phase is silent, the only quantity needed is the signal of the same composition when all the drug is crystalline, which the 75/25 crystalline mixture provides, with no amorphous-plus-crystalline standards and no multivariate model. The spike test checks additivity inside the real matrix, and running all three techniques on the same withdrawn samples allows direct comparison of the time courses.

④ How it differs from earlier work. This is the first application of SONICC to a solid dispersion. Earlier SONICC work concerned single-component amorphous griseofulvin, and earlier SHG quantification by other groups concerned blends of crystalline drug with polymer. The calibration strategy also differs from that of PXRD and Raman, which here needed separate dispersion-based standards.

Experimental analysis

Setup in brief. One drug (naproxen) and one polymer (HPMCAS AS-MF) were studied as cryomilled physical mixtures (PM) and as a rotary-evaporated solid dispersion (SD) at 75 wt% polymer, all sieved below 105 µm, and each was measured by SONICC, PXRD and Raman. The results follow the paper's order: the fresh dispersion, the calibration and validation on physical mixtures, and the crystallization time course.

Result 1: a dispersion that looks amorphous already contains crystals. Figure 2 compares the fresh dispersion with a physical mixture of the same composition (Table A).

Table A. Fresh dispersion versus physical mixture at 75 wt% HPMCAS–25 wt% naproxen (from Figure 2 and the Results text; peak positions other than 856 and 863 cm⁻¹ are approximate readings from the figure).

By PXRD and Raman the dispersion "appears to be amorphous", while the SONICC images "clearly reveal" that it "does in fact still contain a significant fraction of crystalline naproxen". The authors attribute the miss to dilution: the drug is "heavily diluted by the polymer, which most likely explains the lack of detection". They assign the SHG to naproxen because the same material later developed naproxen PXRD peaks. The crystalline content was not checked by an independent method. On the SONICC scale the 0 h value was about 24% of the drug (Figure 7), about 6 wt% of the powder. Note by the AI writer (from card note X9): that is close to the 5 wt% below which the PXRD calibration blends showed no peaks, so this result shows SONICC seeing crystals near the edge of PXRD's range, not at trace level.

Result 2: the SONICC calibration is linear and comparable in quality to PXRD and Raman. Figure 3 plots SHG-measured against nominal crystallinity over 0–100%, with a 0–25% insert; Figure 5 shows the PXRD and Raman calibrations (Table B).

Table B. Calibration statistics for naproxen–HPMCAS physical mixtures (slope, R² and RMSEE from Table 1; band widths read from Figures 3 and 5, approximate). The text also gives Q² 0.97 for PXRD and 0.99 for Raman.

All three methods give slopes near 1 and high $R^2$. SONICC's RMSEE (2.68) lies between PXRD (4.10) and Raman (2.22), and the prediction bands rank the same way. The SHG points sit close to the identity line at every level, for example about 13–15 at 15%, 44–52 at 50% and 88–97 at 90%, with scatter growing at higher content. The authors read this as SHG intensity varying linearly with naproxen content, with HPMCAS that "does not appear to interfere". PXRD had a specific weakness at the low end: blends below 5 wt% naproxen showed no crystalline peaks, so a full-pattern OPLS fit was needed. Two printed values need care. For 0–25%, the text gives slope 0.92 and $R^2$ 0.99 against Table 1's 0.941 and 0.996 (card note X3); the table is used here. The abstract's "root mean square error of prediction" of 2.7% over 0.1–100 wt% appears to be the rounded RMSEE, a fit error rather than a validated prediction error (card note X4).

Result 3: the prediction set is read within about 5–10%. Table C gives the three compositions left out of calibration.

Table C. Predicted crystallinity of the independent prediction set (from Table 2; the last column is computed by the AI writer as predicted divided by nominal, minus 1).

The authors call SHG's errors (about 10% at the lowest level, 5% or less at the others) "comparable with the other techniques" and the values "very close to the theoretical values considering the fact that there are undoubtedly errors associated with preparation of the samples". The last column supports this: SHG is not worse than Raman at 18% and 83%, and PXRD gives no value at 3.5%, in line with its lack of peaks below 5 wt%. Note by the AI writer (not discussed in the paper): all three methods over-read the 83% sample, and SHG and Raman both over-read the 18% sample. When independent techniques err in the same direction, part of the error may lie in the samples; "actual" crystallinity is the weighed composition and was not checked after cryomilling (card note X12). The Discussion cites Table 1 for these values, which are in Table 2 (card note X6).

Result 4: single crystals are visible at 0.1%, and the calculated limit is 10 ppm. In Figure 4, pure crystalline naproxen gives SHG throughout the field, while the 0.1% blend shows about six discrete bright regions (count read from the figure). The depth profile of one crystallite is a single peak of about 100 × 10³ counts/s near 0 µm, about 20–25 µm wide at the base, with nothing elsewhere between about −120 and +120 µm. The authors take this as "clearly indicating that HPMCAS does not interfere with the SHG signal and that miniscule levels of crystallinity can be readily detected". The single-voxel calculation gives 1 × 10⁻³% crystallinity, that is, 10 ppm. Table D sets these beside the detection levels the paper cites.

Table D. Detection levels for crystallinity: values measured or calculated in this study and values the paper cites (Results and Discussion sections).

Two claims are easy to merge here. Single crystals imaged at 0.1% in 99.9% polymer is direct evidence and already lies well below the PXRD limits in the table. The 10 ppm figure is a calculated threshold, 100 times below any level imaged, with unprinted inputs (card note X10).

Result 5: added crystals add up in a spiked dispersion. A partially crystallized dispersion read 22.2% by SONICC; after a known amount of crystalline naproxen was added it read 39.1%, against a theoretical 41.1%. The authors report "a recovery of approximately 93%" (later "greater than 90%"), "indicating the linear additivity of the initial crystallinity and the added crystalline material". The 93% cannot be reproduced from the printed values (card note X5): measured over theoretical total is 39.1/41.1 = 95.1%, and recovery of the added part is (39.1 − 22.2)/(41.1 − 22.2) = 89.4%. Either way recovery is about 89–95%, so approximate additivity stands, but the stated value has no visible derivation.

Result 6: during storage at 60 °C, SONICC reads crystallinity first and then tracks PXRD and Raman. In Figure 6, PXRD showed no peaks before 2 h, a weak peak at about 19° 2θ at 2 h, and peaks at about 19, 22.5 and 23.7° 2θ by 12 h, all weaker than in the physical mixture. In Raman, a shoulder at 863 cm⁻¹ appeared at 2 h on the broad 856 cm⁻¹ band and grew into a peak. SONICC showed sparse bright points at 0 h and more and larger bright regions at 2 h. With RMSEE of 5% (PXRD) and 7.4% (Raman) for the dispersion-based models, the authors state that crystallinity "could not be estimated for either technique until the 2 h time point" (Table E).

Table E. Crystallinity of the 75 wt% HPMCAS–25 wt% naproxen dispersion (as % of the drug) during storage at 60 °C (read from Figure 7, approximate; "–" means no point plotted). SONICC is normalised to the 75/25 crystalline physical mixture; PXRD and Raman use dispersion-based models.

All three methods show the same rising trend, and at 75 wt% polymer crystallization was still incomplete after 48 h at 60 °C. The authors describe the agreement as "good" (Results, Abstract) or as matching "reasonably well" (Discussion), with SONICC "falling in between" the other two, and call discrepancies of this size "common" (refs 16, 34, 35). The ordering holds from 4 h; at 2 h SONICC (about 31) is above both PXRD (about 27) and Raman (about 26) (card note X14). The spread at 48 h, about 44 to about 54, shows that the methods agree on the shape of the curve more closely than on its level. The first two SONICC points, about 24% and 30%, are the part of the curve only SONICC sees; the paper does not show what the dispersion models returned at 0 and 1 h.

Controls and what they rule out. Pure HPMCAS gives the subtracted background, ruling out a significant polymer signal. The same-composition physical mixture in Figure 2 shows what crystalline naproxen looks like in each technique. The later naproxen PXRD peaks tie the early SHG spots to naproxen crystals. The prediction set and spike test check the calibration on samples that did not define it. The controls do not rule out differences in crystal size or orientation between dispersion and standard, and the dispersion readings were never tested against the dispersion-based standards used for PXRD and Raman (card note X15).

Discussion

Where the approach applies. Three conditions are built into the method. The drug must crystallize in an SHG-active, noncentrosymmetric space group, which covers the large majority of chiral compounds but "routinely does not arise for achiral targets". The matrix must be nearly SHG-silent: amorphous polymers qualify, but crystalline chiral excipients "will potentially interfere". And crystals must exceed about 100 nm (Wanapun 2010); smaller nuclei "are unlikely to be detected". Within these conditions SONICC offers what ensemble methods do not: a map of where crystals sit, measurements in seconds to minutes, no need for thin or transparent samples, and nondestructive analysis. SEM and TEM "may be suitable" for smaller crystals at high number densities, but SONICC can find rare, isolated crystals that a small electron-microscopy field would miss.

The scaling question. The Discussion states that "it is clear that SHG scales linearly over the range of percent crystallinity in these measurements of solid dispersions", and that "it is reasonable to expect linear scaling behavior to emerge as the general trend". The Conclusions call this "helping to resolve a fundamental scaling ambiguity". The evidence is strong for the physical mixtures (slope 0.98, $R^2$ 0.998). For the dispersion itself, the support is agreement with PXRD and Raman over about 24–54% crystallinity of the drug, without a regression (card note X8). Within the theory section's framework, linearity means the naproxen microcrystals behave as incoherent collections of domains; the crystal microstructure that would confirm this was not measured.

Calibration without amorphous standards. The authors list as an advantage over Raman and PXRD that SONICC can use "the pure 100% crystalline material or a crystalline-polymer physical blend as the standard", without chemometrics or amorphous–crystalline calibration samples. This would save real effort, since such standards must be made for each dispersion composition. The paper itself names the conditions: the SHG signal is "sensitive to particle size", so standards must match the samples; larger crystalline domains give more SHG, up to the coherence length (LaComb 2008); and the random-orientation assumption "might not be held for a very sparse crystallite sample such as early kinetics of crystallization", which is the regime where SONICC is most attractive.

What is unresolved. Linearity at low crystallinity inside a dispersion was not tested, since the dispersion data start at about 24% of the drug. SONICC was not compared with dispersion-based standards. Crystallite size and orientation, the SHG response to particle size and the response to laser power were not measured. The origin of the crystals in the fresh dispersion was not examined. Note by the AI writer (not discussed in the paper): the dispersion was cryomilled after drying, and the group's earlier work showed that cryomilling changes griseofulvin crystallinity, so incomplete amorphization during rotary evaporation and a change during milling or handling are both possible; the paper gives no basis for choosing between them. The authors also see "potential utility" for online monitoring, but samples were withdrawn and measured at intervals.

What it suggests for formulation. The authors' recommendation concerns dispersions at low drug loading, where SONICC "would be especially advantageous in monitoring minute levels of crystallinity" and could spare long storage studies while polymer and process are optimised. Note by the AI writer (not stated in the paper): a dispersion that passes PXRD and Raman as amorphous can still carry crystals, here about a quarter of the drug, and at lower loading the same fraction of the drug would sit further below the PXRD limit, so the risk of missing seeds grows as loading falls. In practice, SONICC readings on stored dispersions are best treated as a trend anchored by a physical-mixture standard, and the SHG activity of the drug's crystal form and of any crystalline excipient should be confirmed first. The authors' framing is balanced: SONICC is "arguably best used as a complement to conventional analyses, rather than as a replacement".

Limitations

Limitations stated by the authors. The authors list three general limitations. SONICC applies only to compounds that crystallize in SHG-active noncentrosymmetric space groups. "With the current instrumental setup, chemical or structural information (beyond an assessment of % crystallinity) is not directly available", which is why they call it "arguably best used as a complement". And crystalline chiral excipients "will potentially interfere". For quantification they add: differences in crystallite size between dispersion and standard ("there can be differences", a factor that also affects PXRD and Raman); the assumption of uniformly distributed orientations, which "might not be held" for sparse early crystals; sensitivity to particle size, requiring matched standards; a minimum detectable crystal size of about 100 nm; and a detection limit raised by "the nonzero background from the polymer". They also acknowledge "undoubtedly errors" in sample preparation.

The AI writer's own judgement (1): what the dispersion data show. The card's overall assessment is moderate: strong for physical mixtures, weaker for the dispersion. Linear scaling "in solid dispersions" rests on cryomilled physical mixtures; for the dispersion there is only agreement over about 24–54%, with no regression (card note X8). Earlier detection in the dispersion is at about 6 wt% crystalline naproxen in the powder, close to the PXRD limit, not at trace level; the 0.1% and 10 ppm statements belong to physical mixtures (card note X9). SONICC and the reference methods used different calibration routes in the time course, so the claimed advantage of crystalline standards remains untested (card note X15).

The AI writer's own judgement (2): numbers and conditions. The 10 ppm limit is calculated, not imaged (X10); the 93% spike recovery recomputes to 95.1% or 89.4% (X5); the text and Table 1 disagree on the 0–25% slope (X3); the abstract's 2.7% "prediction" error is the RMSEE (X4); the Discussion cites the wrong table (X6); the PXRD current is printed as "30 mV" (X7); and Eqs. 4–6 contain slips (X1, X2). None reverses a conclusion, but exact figures should be quoted with these caveats. "Actual crystallinity" is the weighed composition, not verified after cryomilling, and all three methods were calibrated to it, so a shared composition error would not appear as disagreement (X12). Storage humidity, container and the spiked sample's history are not printed (X13). One drug, one polymer, one drug loading and one temperature cannot support linear scaling as "the general trend"; the authors' own hedge, "it is reasonable to expect", is the right strength.

Conclusion

SONICC can quantify crystalline naproxen in HPMCAS powders. In cryomilled physical mixtures its signal followed crystalline content linearly over 0–100% (slope 0.98, $R^2$ 0.998, RMSEE 2.68), with accuracy between PXRD (RMSEE 4.10) and Raman (RMSEE 2.22), and it read an independent prediction set within about 5–10%. Because amorphous material gives no net SHG, single crystals stood out at 0.1% in 99.9% polymer, and the calculated single-voxel limit was 10 ppm. In a 75 wt% HPMCAS–25 wt% naproxen dispersion that PXRD and Raman classed as amorphous, SONICC showed crystals immediately after preparation, gave readings before the other methods could, and then tracked their kinetics over 48 h at 60 °C. In the authors' words, SONICC "has been found to enable sensitive quantification" of crystalline material in blends and dispersions.

The evidence is uneven: linear scaling and trace sensitivity are well supported in physical mixtures, while in the dispersion the method agreed with PXRD and Raman over about 24–54% and detected crystals at about 6 wt% of the powder, earlier than the other methods but not at trace level. For formulation work, the lasting message is that "amorphous by PXRD and Raman" is not the same as "free of crystals", and that for SHG-active drugs an SHG check can expose seeds that would otherwise go unnoticed.