Engineering drug crystals so that they dissolve faster into the polymer melt during hot melt extrusion

Background and motivation

Hot melt extrusion (HME) makes amorphous solid dispersions (ASDs) by feeding drug and polymer powders into a heated screw, forming a homogeneous melt and extruding it. The drug enters as crystals, so heat and mixing must either melt the drug or dissolve it in the molten polymer before the product leaves the extruder. Too little temperature or mixing leaves residual crystals that harm physical stability and dissolution; too much temperature or time degrades drug or polymer. The two risks sit at opposite corners of the operating space, and the authors call processing below the drug's melting point "highly desirable" for that reason. C2 Below the melting point the drug can only become amorphous by dissolving in the polymer melt. Its solubility in the melt is read from the temperature–composition phase diagram, built from melting point depression and modelled by Flory–Huggins theory or PC-SAFT; the lowest workable temperature for a given composition is the formulation critical temperature $T_c$ (Moseson and Taylor 2018, ref 9). C1·C3

Thermodynamics says whether the crystals can dissolve; kinetics says whether they do so within the residence time. If dissolution into the melt follows a Noyes–Whitney-type law, the rate scales with crystal surface area, so the particle size distribution (PSD) of the incoming drug is a critical material attribute. C4 Small particles are the obvious answer, and the micronized lot used here did become amorphous within the first sampling time. But particles below about 30 µm have low bulk density, high compressibility and high cohesion, which makes them hard to feed from a hopper; blending with excipients helps little at high drug loading and adds a step to continuous manufacturing (refs 44, 47–51). C5·R21 The question is therefore where the "sweet spot" lies between powder flow and amorphization rate, and whether crystals can be designed that do both.

The authors' earlier work on indomethacin pointed to a second lever. Crystals dissolving into a PVPVA melt fragmented: residual crystals in extrudates showed amorphous channels under transmission electron microscopy, fragmentation was seen at several length scales without shear, and a Monte Carlo simulation supported faster dissolution at defect sites (Moseson 2019, ref 42; Moseson 2018, ref 115). C6·C50·R24 Surface pits and roughening also accelerate the dissolution of bicalutamide single crystals in water (Maddar 2017, ref 58), and crystallization can be run to produce more defects, through growth rate or agglomeration (refs 59–64). C6 If defects help, a large crystal with many internal boundaries might flow like a large particle yet dissolve like a small one.

A modelling gap completes the motivation. The HME process model of Schittny et al. (ref 73) follows the surface area of a constant number of particles. Fragmentation and breakage change the number of particles, so the authors chose a population balance model, which tracks how many crystals of each size exist over time and can include breakage as well as dissolution. C7 They frame it as a step toward a "digital twin" of the process, a model trained by parameter estimation that could replace experiments in process design. C9

The study uses bicalutamide (BCL), a poorly water-soluble drug with a melting point of about 194 °C, and PVPVA (Kollidon VA64), the most common HME polymer. C8·M1·M2 Its goal, in the authors' words, is to identify the attributes of drug crystals that give rapid dissolution during HME. They recrystallized micronized BCL four ways to obtain lots of different size, shape, agglomeration and surface quality, extruded each at the formulation critical temperature over a range of residence times, measured the residual crystallinity, and built the population balance model. A1·A2·A4

Background concepts

Melting and dissolution regimes, and the formulation critical temperature. An extruder can make an amorphous product in two ways: by melting the drug (above its melting point $T_m$) or by dissolving it in the polymer melt (below $T_m$). In the second, "dissolution regime", the temperature must be at least the solubility temperature of the crystalline drug at the formulation's composition, called the formulation critical temperature $T_c$, and above the polymer's minimum processing temperature, which a viscosity limit sets. Figure 12a draws this as an operating map of temperature against residence time, with regions for thermal degradation, melting, dissolution and suspension (crystals left over); smaller or faster-dissolving particles move the line that separates "still crystalline" from "fully amorphous" to shorter times. C36·C40

Melting point depression and the Flory–Huggins model. A crystal mixed with a polymer it can dissolve in melts, or rather disappears, at a lower temperature than the pure crystal. The authors measured this depressed melting point for each composition and fitted it with the Flory–Huggins expression (eq 5):

Here $T_c$ is the depressed melting point (the solubility temperature), $T_m$ the melting point of the pure drug, $R$ the gas constant, $\Delta H$ the drug's heat of fusion, $\varphi$ the drug volume fraction, $m$ the ratio of the polymer segment volume to the drug molecular volume (the drug molecular volume serves as lattice volume), and $\chi$ the Flory–Huggins interaction parameter. In plain terms: the more polymer there is, and the more favourably drug and polymer interact (a negative $\chi$), the lower the temperature at which the crystals can fully dissolve. Rearranged, the same equation gives a straight line whose slope is $\chi$ (SI Figure S2c). E5·E20 The glass transition of the mixtures was described by the Gordon–Taylor equation with a density-based constant (eq 6):

with $w$ the weight fraction, $\rho$ the true density and the subscripts 1 and 2 the two components. In plain terms: the $T_g$ of the mixture is a weighted average of the two pure-component values. E6

Dissolution into a melt. The authors use the Noyes–Whitney equation with the Nernst–Brunner diffusion layer as their framework (eq 18), together with the Stokes–Einstein equation for the diffusion coefficient (eq 19):

Here $C$ is the concentration of dissolved drug, $C_{sat}$ its equilibrium solubility in the molten polymer, $A_S$ the crystal surface area available for dissolution, $h$ the thickness of the boundary layer at the crystal surface, $V$ the volume of the liquid phase, $D$ the diffusion coefficient, $k_B$ the Boltzmann constant, $T$ the temperature, $\eta$ the viscosity and $r$ the radius of the diffusing species. The left-hand side is printed as $dC/dT$ although the text defines it as the change of concentration with time. In plain terms: dissolution is faster the more crystal surface is exposed and the further the melt is from saturation, and slower the more viscous the melt. At $T_c$ the melt is most viscous, diffusion slowest and the gradient smallest, so the authors expect the slowest dissolution that still ends in a fully amorphous product; they also note that Stokes–Einstein has known limits at high viscosity and that real extruders do not hold constant temperature or sink conditions. E18·E19·C37·C38·C39·X11

Describing a crystal population. Laser diffraction gives the volume-weighted size distribution, summarized by $D_{10}$, $D_{50}$ and $D_{90}$, the sizes below which 10, 50 and 90% of the volume lies; the ratio $D_{90}/D_{50}$ describes how wide the coarse side of the distribution is. Image analysis (Morphologi G3) adds number-based shape factors computed from each particle's projected area $A$ and perimeter $P$ (eqs 1–3):

In plain terms: circularity is 1 for a circle and falls for elongated or ragged outlines; convexity is 1 for a smooth convex outline and falls for rough or indented edges; the circular equivalent diameter is the diameter of a circle with the same area. The percentage of agglomerates was counted by hand from the images (eq 4: agglomerated crystals divided by all crystals counted, times 100). E1·E2·E3·E4

Population balance modelling. A population balance model (PBM) describes a crystal population by its number density $n(t,L)$, the number of crystals per unit length of the size axis per cubic metre of melt, as a function of time $t$ and crystal length $L$. Events such as nucleation, growth, dissolution, agglomeration and breakage enter as terms that move crystals along the size axis, create them or remove them, and a mass balance links the crystals to the dissolved drug. The authors kept two events, dissolution and breakage (eq 7):

In plain terms: the number of crystals of size $L$ changes because crystals shrink through that size (first term), because larger crystals break into fragments of that size (second term), and because crystals of that size break and leave it (third term). The size-dependent dissolution rate $\alpha (L)$, the fragment distribution $b$ and the breakage selection function $S$ are defined in the Methods below. E7

Methods in detail

The study has three parts: making crystal lots that differ in defined ways, measuring how fast each lot becomes amorphous in an extruder run at a deliberately slow condition, and modelling the crystal population during that process. The method flow below shows how they connect.

Contribution 1: crystal lots that differ in one attribute at a time

Problem. To separate the effect of particle size from that of crystal "quality", the authors needed lots of the same drug and polymorph whose median size is similar but whose size distribution, agglomeration and surface quality differ, plus a much larger and a much smaller lot as references. A1

What they did. The starting material was micronized BCL as received (Lot L3). M3 All recrystallizations started from a BCL solution in ethanol saturated at 60 °C (26.8 mg/mL), and every lot was filtered, dried and sieved to remove oversized agglomerates. P1

• Lot L38, cooling crystallization. The solution was stirred at 280 rpm in a 500 mL jacketed vessel and cooled to 10 °C without temperature control, a fast cooling; several batches were combined. P1
• Lot L93, direct nucleation control (DNC). Same vessel and stirring, cooled at 0.1 °C/min to 10 °C with heating–cooling cycles triggered by a focused beam reflectance measurement (FBRM) count threshold of 1500 counts/s. Limiting the number of crystals lets each one grow large. In the run shown in SI Figure S1, the count peaked at about 4100 counts/s after nucleation and settled at about 2000 counts/s while the temperature cycled up to about 42 °C and back down to 10 °C. P2·R18
• Lot L42, growth and milling. The saturated solution was left to cool to room temperature overnight on a flat surface without stirring, giving crystals of about 1–2 mm, which were then milled in toluene with an immersion mill (5000 rising to 11 000 rpm over 12 min). P3
• Lot L37, continuous crystallization. The solution was pumped at 30 mL/s through a 1.25 L oscillatory flow baffled reactor (15 mm baffles, spaced 1.5 diameters) with three temperature zones of 18, 30 and 20 °C; the warm middle zone prevents clogging and adds a small thermal cycle. P4

Each lot was characterized by triplicate laser diffraction (dry dispersion) and BET surface area, by Morphologi image analysis of at least 3000 crystals, by SEM and by FT4 powder rheometry (conditioned bulk density, compressibility at 15 kPa, flow function and cohesion). Solid form was checked by PXRD, by DSC at 1–20 °C/min and by 13C, 1H and 19F solid-state NMR. P5·P6·P7·P8·P9·P10·P11·P12

Why it works. The four routes produce, by design, different kinds of particle at similar median size: fast cooling gives rough surfaces, continuous crystallization gives agglomerates of small crystallites ("spherical" agglomerates that form here without a bridging liquid), milling gives a broad distribution, and DNC gives large, well-healed crystals. The authors treat surface roughness (L38) and grain boundaries in agglomerates (L37) as the two "types of crystal defects" of the study. C11·C12·C13·C15·C42·C59 Note by the AI writer (not discussed in the paper): these defect types are inferred from SEM appearance and from the agglomeration count; no measurement of defect density was made, and PXRD, DSC and NMR show no difference between the lots other than a small pre-melting DSC event in L38. X6

Contribution 2: measuring amorphization at the slowest workable condition

Problem. Above $T_c$ crystals dissolve quickly, and differences between lots would be hard to see. The authors wanted a condition where dissolution is slow but still complete, so that kinetics can be followed over minutes. C23

What they did (phase diagram). Cryomilled physical mixtures of BCL and PVPVA (30/70 to 90/10, each in triplicate) were heated in DSC at six rates from 0.5 to 10 °C/min. The temperature at which the last crystal disappeared (the melting point offset) depends on heating rate, so it was fitted with a second-order polynomial and extrapolated to zero heating rate. The extrapolated values define the solubility line; Flory–Huggins fitting gave $\chi$ = −1.57 (R² = 0.994), and $T_c$ at 30% drug is 145 °C. P14·R8·R9 As a check by the AI writer, eq 5 with $\chi$ = −1.57, $T_m$ = 194.1 °C, $\Delta H$ = 45.9 kJ/mol, $m$ = 46,610/319 and a volume fraction of 0.2725 computed from the amorphous densities in Table SI gives a $T_c$ of 144.3 °C at 30% drug, close to the measured 145 °C; the paper does not state how weight fractions were converted to volume fractions. E5

What they did (extrusion). Blends of 30% BCL crystals and 70% PVPVA were tumble-blended and run in a 5 mL batch micro-extruder (Xplore) with conveying screws at 50 rpm. The melt temperature was held at 145 ± 1 °C with a set temperature of 150 ± 1 °C. The extruder recirculates the melt; the residence time (2 to 20 min) is the moment the recirculation valve is opened, and extrusion lasted about 1 min after that. Extrudates were cryomilled and analysed by PXRD: the area of the 17.2° 2θ peak was calibrated from 0 to 65% crystalline content (R² = 0.9952) using physical mixtures of crystalline BCL and a fully amorphous ASD; the limit of detection is about 1% and the limit of quantification about 3%. Each sample was measured in triplicate. P15·P16

What they did (hot-stage microscopy). Crystals of L37, L38 and L42 were suspended in PVPVA films (10:1), held at 170 °C without mixing and photographed under polarized light for 30 min. The higher temperature brings dissolution without shear into an observable time frame. P17

Contribution 3: a population balance model with breakage

Problem. A model that keeps the number of particles constant cannot describe crystals that fragment. The authors needed a model that lets crystals both shrink and break, starts from each lot's measured PSD, and can be compared with the measured crystallinity. C7

What they did. The number balance (eq 7, above) is coupled to a mass balance for the dissolved drug (eq 8):

where $k_V$ = 0.5236 is the shape factor of a sphere and ${\rho }_c$ the true density of the BCL crystals. In plain terms: the rate at which drug appears in the melt equals the rate at which crystal volume disappears, summed over all sizes. E8·P18 The dissolution rate depends on the distance from saturation and, through an empirical correction, on size (eq 9):

where $k_d$ is the dissolution rate constant (µm/s) and ${\alpha }_{d,1}$, ${\alpha }_{d,2}$ are a size-dependent coefficient and exponent. $C_{sat}$ was fixed at 0.3 g/g, the drug content of the formulation, so dissolution can in principle consume all crystals. In plain terms: crystals shrink at a speed proportional to how far the melt is from saturation, modified by a power of size. E9 When a crystal breaks, it splits symmetrically into two fragments of equal volume, of size $L/2^{1/3}$, spread by a Gaussian with a standard deviation of one-eighth of the fragment size (eq 10):

In plain terms: fragments are not all of one size but scatter by about 12.5% around the equal-volume size; the authors report that this spread, optimized in unpublished work, has little effect on the breakage rate. E10·C10 Which crystals break, and how often, is set by a hyperbolic-tangent selection function (eq 11):

with breakage rate constant $k_{br}$ and a critical breakage size $L_{crit}$ = 5 µm "based on experimental observation". In plain terms: at 5 µm the function is half of its maximum, larger crystals break almost at the full rate, and smaller ones break less often; at zero size it is still about 0.43 of the maximum (SI Figure S5a). E11·R19 Crystallinity is computed from the dissolved concentration (eq 15):

In plain terms: 100% at the start, when nothing has dissolved, and 0% when the dissolved drug reaches 0.3 g/g. The zeroth and third moments of $n(t,L)$ give the total crystal number and volume. The equations were solved with a high-resolution finite volume method on a validated grid for 20 min, starting from each lot's measured PSD (eqs 13, 14, 16). L3 was not simulated. E15·E16·P18

Three simulations followed. Simulation 1 had dissolution only, with $k_d$ = 0.5 or 4 µm/s taken from crystallization literature, ${\alpha }_{d,1}$ = 0.5 and ${\alpha }_{d,2}$ = −0.8. Simulation 2 added breakage with $k_{br}$ = 0.1 and $k_d$ = 0.5 µm/s. For simulation 3, the authors argued that defect-driven fragmentation, for example at grain boundaries, takes place in crystals made of many agglomerated crystallites, "likely leading to faster dissolution rates" (Figure 7), and therefore multiplied the selection function by each lot's agglomeration percentage (eq 17). A4·C29

In plain terms: with the same $k_{br}$, a lot that is 88.6% agglomerated breaks far more often than one that is 1.8% agglomerated. Whether the percentage enters as a number such as 88.6 or as a fraction such as 0.886 is not stated. The four parameters $k_d$, $k_{br}$, ${\alpha }_{d,1}$ and ${\alpha }_{d,2}$ were fitted to the measured crystallinity by minimizing the summed squared difference between experimental and simulated values (eq 12), using a genetic algorithm (more than 15 000 function evaluations) followed by a gradient-based refinement, with 95% confidence intervals from lsqnonlin and nlparci. E17·E12·P19·X10

How it differs from earlier work. Compared with the constant-particle-count HME model, the PBM lets the number of crystals rise through breakage and fall through dissolution, and it starts from the full measured PSD rather than a single size. The step that ties the model to particle engineering is eq 17, which brings one measured particle attribute into the breakage rate. C7·C49 Note by the AI writer (not discussed in the paper): the printed sign conventions do not line up. With $C$ below $C_{sat}$, eq 9 gives a negative $\alpha$ (SI Figure S5b plots negative rates), which in eq 8 as printed would make $C$ fall, while the text and eq 15 have $C$ rising as crystals dissolve. In eq 7 the symbol $L^{\prime }$ is the parent size in the integral, but in eq 10 and the text it is the fragment size. The model as coded cannot be reconstructed exactly from the printed equations, although its intended behaviour is clear from the text. X11·X12

Experimental analysis

The lots: same median size, different coarse end and agglomeration

Table A collects the particle attributes. As received, BCL was a micronized powder with a $D_{50}$ of 3.51 µm and a BET surface area of 1.91 m²/g. R1 Three recrystallized lots share a $D_{50}$ of 37–42 µm, but they differ where it matters for the argument: L42 has a $D_{90}$ of 175 µm and a $D_{90}/D_{50}$ of 4.14, against 109 µm and 2.94 for L37 and 85.6 µm and 2.25 for L38; L37 is 88.6% agglomerated, L38 45.5% and L42 8.8%. L93 is the large reference, with a $D_{50}$ of 92.7 µm and only 1.8% agglomerates. R1·R2 The measured volume PSD of L37 also has a small coarse tail near 1000 µm (Figure 2b), which the authors later call "likely an artifact" of aggregation in the measurement. R4·C27

Table A. Particle attributes of the five BCL lots (Table 1, mean ± SD, n = 3; Table 2, number-based medians of at least 3000 crystals; flow function from the text, L42 read from Figure 3c, approximate). R1·R2·R5

SEM (Figure 2a) shows what the numbers summarize: tabular L38 crystals with rough surfaces and some agglomeration, which the authors attribute to the fast cooling; agglomerated, roughly spherical L37 particles in which the tabular habit of form 1 is still visible, with generally smooth surfaces; irregular L42 particles of very different sizes, the roundest of the recrystallized lots; and large, smooth, elongated L93 crystals. The authors read rough surfaces as "suggesting high defect density" and smooth ones as suggesting low defect density. R3·C12·C13·C14·C15 Note by the AI writer (not discussed in the paper): the caption of Figure 2 lists panels (c), (d) and (e) as HS circularity, convexity and CE diameter, but the axes read convexity, CE diameter and HS circularity, in that order. X1

Every recrystallized lot flowed far better than L3: conditioned bulk density rose from 0.56 to 0.72–1.12 g/mL, compressibility at 15 kPa fell from 56% to 6–29%, the flow function rose from 0.9 ("not flowing") to 3.1–5.2 for the 40 µm lots and 8.2 for L93, and cohesion fell from 5.72 to 0.58–1.59 kPa (Figure 3). R5·C16 L37 packed densest (about 1.12 g/mL) but had the lowest flow function of the recrystallized lots (about 3.1), which the authors attribute to agglomerates that are "likely" to interlock mechanically. R5·C18 Two statements in this part of the text do not match Figure 3 exactly: L93 is said to outperform the other lots "in each of the powder characteristics", but L37 has the higher bulk density; and L42 is said to flow worse than lots of similar $D_{50}$ "(L38 and L42)", a self-reference, while its flow function and cohesion are better than those of L37. X3·X4

Solid form

PXRD patterns of all lots matched BCL form 1 (single-crystal structure JAYCES01), with stronger 6.1° and 12.3° 2θ peaks from preferred orientation of the tabular crystals (SI Figure S3). DSC gave similar melting points and enthalpies of fusion for all lots, about 43–47 kJ/mol with no trend across heating rates (SI Figure S4c). At 20 °C/min, L93 melted over a broader range, and L38 showed a small endotherm just before the main melt that was absent at 1 °C/min; the authors say it "may signify" a trace of a metastable polymorph or of amorphous material that recrystallized during heating. R6·C21 Solid-state NMR spectra had identical chemical shifts and sharp lines, and the authors conclude that no amorphous content was detectable in any lot. Figure 4 shows L93 only in the 13C panel, not in the 1H and 19F panels. R7·C20·X7

The phase diagram and the choice of 145 °C

The extrapolated melting offsets define the solubility line in Figure 5: about 145 °C at a drug weight fraction of 0.3, about 166 °C at 0.5, about 189 °C at 0.8 and about 194 °C for pure BCL, with measured $T_g$ values falling from about 104 °C (PVPVA) to about 53 °C (BCL), slightly below the Gordon–Taylor line. R9 The Flory–Huggins fit gave $\chi$ = −1.57, and the authors take the diagram as confirming drug–polymer miscibility at HME temperatures. R8·C22 At 30% drug the melting point is depressed by about 50 °C, to 145 °C. That temperature was chosen as the process temperature because it is the minimum at which a fully amorphous product can form, so dissolution there is as slow as it can be while still going to completion. R9·C23 The paper prints the BCL melting point as 194 °C, 195 °C and 194.1 ± 0.1 °C in different places, and the PVPVA $T_g$ as 105 °C and 104.2 ± 0.4 °C; the SI table values are used here. X2

Amorphization in the extruder

Figure 6 is the central experiment, and Table B gives its values. L3, the micronized lot, showed no measurable crystallinity at the first sampling time, 2 min. R10 Among the 40 µm lots, L37 fell from about 14.2% at 2 min to below detection at 5 min, and L38 from about 15.3% at 2 min to about 5.9% at 5 min and below detection at 6 min. L42 was much slower, with about 18.0% left at 5 min and about 2.5% at 20 min (the text gives 10% at 10 min and 2% at 20 min). L93, the largest lot, kept about 15.0% at 20 min. R10

Table B. Residual crystallinity (%) of extrudates made at 145 °C, by PXRD, mean of triplicates, read from Figure 6 (approximate); "–" = not sampled. Zero means below the limit of detection (about 1%); values below about 3% are below the limit of quantification. R10·X8

The authors draw two conclusions from Figure 6. First, size matters as expected: every recrystallized lot dissolved more slowly than L3, and L93 most slowly. Second, at the same $D_{50}$ and similar surface area, L42 was much slower than L37 and L38, and its broader PSD is "the likely source": as the fines disappear, the large particles that remain dissolve slowly, so "simple measurements of particle size D50 and surface area are not indicative of the crystal dissolution rate alone". C24·C44 They then compare L37 and L38: "despite having nearly identical PSDs", L37 reached zero crystallinity faster, "indicating that the relative defect density of the agglomerated material was greater than the lot with rough surfaces". C46 Note by the AI writer (not discussed in the paper): the two PSDs share their $D_{50}$ but not their coarse end ($D_{90}$ 109 against 85.6 µm), and the ranking rests on the 5 min point; at 4 min L37 had more crystallinity left than L38 (about 11.4 against 8.2%). X5

What the hot stage shows

Figure 7 follows single crystals at 170 °C without mixing. An L38 crystal shrank in every dimension, and another split into two pieces between 10 and 15 min. L37 agglomerates broke into smaller particles, which then shrank. In L42 the fines vanished quickly while a large crystal hardly changed in 30 min. R11·C25 The authors take this as the quiescent form of fragmentation: dissolution attacks defects and surface-energy heterogeneity and separates crystals, which they see as one of two sources of breakage in an extruder; the other is mechanical, when particles meet the mixing elements or exceed their critical breakage stress. C45 These images were taken 25 °C above the extrusion temperature, without shear and without L93 or L3. X18

Simulations 1 and 2: the model needs breakage

With dissolution alone, no lot dissolved in 20 min (Figure 8, Table C). At $k_d$ = 0.5 µm/s the simulated crystallinity after 20 min was about 73% for L37, 65% for L93, 56% for L42 and 26% for L38; at $k_d$ = 4 µm/s it was about 61, 27, 20 and 3%. Total crystal number fell from about ${10}^{14}$ per m³ to about ${10}^{11}$–${10}^{12}$ per m³ at $k_d$ = 0.5 µm/s, and the $D_{50}$ of what remained grew to about 98–127 µm (Figure 11), because small crystals disappear first. R12·R17 The authors conclude that dissolution "is not the only important mechanism and that breakage must be considered". C26 They also note the lack of a clear trend with $D_{50}$: L37 came out slowest because its coarse PSD tail, "likely an artifact" of the measurement, becomes a growing share of what remains. C27

Adding breakage ($k_{br}$ = 0.1) changed the picture completely (Figure 9). Crystallinity fell to about 50% within about 2 min and to about 0 by about 10 min for all four lots, nearly independent of their starting size, while the number of crystals rose to about ${10}^{20}$ per m³. The remaining crystals were all smaller than 0.1 µm and added up to 0.01 g after at least 99.61% dissolution. R13 The authors read this as a warning about processing at the solubility temperature: dissolution becomes very slow as equilibrium is approached, and many very small crystals with a low driving force "may remain". C28

Table C. Simulated crystallinity (%) after 20 min, read from Figures 8c, 9c and 10c (approximate); simulation 3 also from the text (99.1 and 91.7% dissolved), measured values from Figure 6. R12·R13·R14·R10·X20

Simulation 3: breakage tied to agglomeration fits the four lots

With the agglomeration-scaled breakage function, the fitted parameters are given in Table D. R16 The fitted $k_d$ of 0.1002 µm/s is lower than the values tried in simulation 1, which the authors relate to the high viscosity and different hydrodynamics of the melt compared with stirred crystallizers ("can be understood"). The fitted $k_{br}$ of 0.355 is higher than the 0.1 of simulation 2, which they explain by dissolution enhancing breakage and by deagglomeration, which "may also occur" and happens more easily than mechanical breakage. C30·C31 The two size-dependence parameters have confidence limits far larger than their values, so the size dependence of dissolution "may not be important" or cannot be separated from breakage; the narrow limits of $k_d$ and $k_{br}$ show that both mechanisms are needed. C32·C33

Table D. Fitted parameters of simulation 3 (Table 3). R16

In simulation 3, 20 min was enough to dissolve nearly all of L37 and L38, while L42 reached 99.1% and L93 91.7% dissolution; lots with larger crystals are harder to dissolve completely, and the breadth of the L42 distribution hardly narrows because of its large particles and low agglomeration. R14·C34 The crystal number shows the mechanism at work: for L37 it rose to about ${10}^{18.8}$ per m³ at about 4 min and then fell to about $4\times {10}^6$ per m³ as the fragments dissolved, while for L42 it kept rising to about ${10}^{16.7}$ per m³. R15 The authors describe the lots as "well described" by the model and conclude that this "further confirms the importance of breakage facilitated by particle attributes". C49 Read against Figure 6, the fit gets the order of the lots right but not every point: the simulated L37 and L38 curves are down to about 0.5 and 4% at 4 min, where about 11.4 and 8.2% were measured, and the simulated L93 ends at about 10% against a measured 15.0%; the text's 91.7% dissolved for L93 corresponds to 8.3% crystallinity. R14·X20

Discussion

The authors' picture of crystal dissolution in a melt. Figure 13 sums up the mechanism they propose. Below $T_m$, amorphization is the dissolution of crystals into the melt, and by Noyes–Whitney its rate scales with the exposed crystal surface. What differs between lots is how that surface evolves while the crystals dissolve. C37·C40·C51

In the authors' words, crystals "may fragment or deagglomerate as a result of accelerated dissolution" at defects, and the sites for fragmentation and for mechanical breakage "are likely the same: high energy defect sites", because grain boundaries resist mechanical failure less. C45·C47 They conclude that "particle breakage is exceptionally important in accelerating crystal dissolution rates", and the abstract states that breakage kinetics "were found to dominate the crystal dissolution process, synergistically accelerated by particles with high defect density". C52 This connects to their earlier indomethacin work, where fragmentation was observed in quiescent melts and in extrudates; the present study was designed in part to test whether that matters in a processing environment. C50

What the authors recommend. Four practical points follow in the paper. Crystallization designed to create defects (fast cooling) or grain boundaries (agglomeration, for example continuous spherical crystallization) is called "excellent particle engineering strategies which yield additional benefits": such lots handle and flow better than micronized powder and dissolve faster than similarly sized crystals, so larger particles can be used. C53·C48 PSD and crystal "quality" play a significant kinetic role, so incoming crystals should be monitored and controlled, and "Monitoring a single particle size data point, such as D50, of input raw materials may not be sufficient". C54 Screw design can be optimized for dispersive mixing to promote breakage; higher screw speed "may further improve dissolution rates", which the study did not test, but more speed and specific mechanical energy also mean more chemical degradation. C55 Finally, processing at $T_c$ itself is "not practical for most products": the model leaves very many crystals even after more than 99% dissolution, so "Temperatures above the formulation critical temperature Tc should be utilized". C56 The authors link this to their earlier TEM study of indomethacin–PVPVA, where extrudates processed at $T_c$ for 20 min showed no crystallinity by PXRD, DSC or polarized light microscopy, yet contained residual crystals as small as 5 nm. C57·R20

Micronized drug. L3 became amorphous within 2 min, and the authors grant that micronization "may be an effective processing strategy" to ensure a fully amorphous product or to limit thermal exposure. They weigh it against the special crystallization or energy-intensive milling needed to make such powders, the feeding and blend-uniformity problems they cause, and the shear that may be needed to break their agglomerates in the extruder. C41·R10·R5

Residual crystallinity as a quality attribute. The paper closes its discussion by noting that even trace crystallinity can cost the solubility advantage of the amorphous form, seed crystallization in the solid or in solution, and change in vitro and in vivo performance, and that no generally accepted threshold exists; it has to be set for each drug–polymer system. C58

Note by the AI writer (not discussed in the paper). For a formulator choosing an input specification, the clearest result is the comparison of the three 40 µm lots: neither $D_{50}$ nor BET surface area ranked them (L42 had the highest BET of the three and was slowest), whereas the coarse end of the distribution did. A $D_{90}$ or $D_{90}/D_{50}$ limit on incoming crystals looks like the more useful control for HME at low process temperatures. The flow data add a trade-off map: micronized L3 amorphized fastest but did not flow, L93 flowed best but stayed crystalline longest, and L37 and L38 combined acceptable flow with fast amorphization. R1·R5·R10

Limitations

Limits the authors state. The size dependence of dissolution could not be resolved: "mechanistic information about any size dependency of the dissolution process cannot be gained from this data set". C32 Viscosity, temperature (viscous heating, zone temperature profiles in commercial extruders) and sink conditions are not constant in real extrusion, and these effects are lumped into $k_d$. C38 Screw speed was not investigated. C55 The coarse tail of the L37 PSD is "likely an artifact" of the measurement, yet the model takes it as real large particles. C27 The processing temperature, $T_c$, is not a practical one for most products. C56

The AI writer's own judgement (1): the defect argument. "Defect density" is the label the paper gives to surface roughness and agglomeration, but it was never measured; PXRD, DSC and NMR did not distinguish the lots, and the defect types are inferred from SEM images and the agglomeration count. The ranking of the two defect types, agglomerates over rough surfaces, rests on one sampling time at which L37 was below detection and L38 at about 5.9%; one minute earlier the order was reversed, and the two lots also differ in their coarse end. The broad-PSD effect is well supported; the defect effect is plausible but not shown. X5·X6 The hot-stage images support fragmentation qualitatively but were taken at 170 °C, without shear, for three of the five lots. X18

The AI writer's own judgement (2): what the model shows. The model shows convincingly that, within its structure, dissolution alone cannot remove the crystals in process times and breakage can. It does not show that crystals break inside the extruder: no particle size, count or image of residual crystals in the extrudates was measured. The fitted model was trained on the same crystallinity data it reproduces, so it is a description rather than a validated prediction, despite the "predictive" and "digital twin" framing in the introduction; its fit misses the 4–5 min points of L37 and L38 and the 20 min point of L93. X9·X20 Several details of the model are not fully defined: the scale of the agglomeration percentage in eq 17, the sign conventions of eqs 7–9, the double meaning of $L^{\prime }$, and the parameters behind SI Figure S5b, whose dissolution-rate curve cannot be reproduced from any printed parameter set. The size-dependence exponent was set at −0.8 in simulations 1–2 and fitted at +0.1091 ± 0.595, so even its sign is open. X10·X11·X12·X13·X21

The AI writer's own judgement (3): scope and smaller inconsistencies. The study covers one drug at one loading (30%) in one polymer, at one temperature, in a 5 mL batch extruder with recirculation; values near zero in Figure 6 lie below the limits of detection and quantification. X8 Minor printing issues do not change the conclusions: the Figure 2 caption lists the shape panels in the wrong order, the initial $D_{50}$ values in Figure 11 differ slightly from Table 1, the lot letters in SI Figure S4c disagree with its legend, and the text cites Figure 3b for the flow function (it is Figure 3c) and Figure 10b for the L42 PSD (it is Figure 10a). X1·X14·X15·X16

Conclusion

The paper makes three contributions. First, it produced a controlled set of bicalutamide lots, four of them by recrystallization, that separate median size from size-distribution width, agglomeration and surface quality, and it showed that all of them flow far better than the micronized starting material. R1·R2·R5 Second, by extruding them at the formulation critical temperature, it showed that lots of equal $D_{50}$ can differ several-fold in how much crystallinity remains: the broad-PSD milled lot kept about 18% at 5 min, while the agglomerated lot was below detection and the rough-surfaced lot at about 5.9%. R10·C44·C59 Third, it built a population balance model in which only breakage, scaled by the agglomeration percentage, lets the crystals dissolve in process times, and it used that model to argue that breakage dominates amorphization in HME and that processing slightly above $T_c$ is safer than at $T_c$. R12·R13·R16·C52·C56

For formulation, the message the data support most firmly is that a single $D_{50}$ is not enough to specify crystalline input for HME: the coarse end of the distribution decides how long the last crystals survive. The message about defects, that agglomerated or rough crystals amorphize faster at the same size, is a well-argued hypothesis that the paper supports with one time point, hot-stage images and a fitted model; quantifying defects and observing breakage inside the extruder would be the tests that settle it. C54·X5·X6·X9