When a polymer speeds up crystal growth: PHB and six supercooled organic compounds

Background and motivation

An amorphous form of a poorly soluble drug dissolves faster and reaches a higher concentration than the crystal, which is why amorphous solid dispersions, drug mixed with a polymer at the molecular level, are used to raise bioavailability. The same high energy that gives the advantage also drives the amorphous drug back to the crystal, and once it crystallizes the advantage is lost, so crystallization has to be prevented for the whole shelf life of a product (Section "Introduction", refs 2, 4, 5). C1

Polymers are the standard tool for this, and many studies show better physical stability with a polymer present. How they work is, in the authors' words, "poorly understood". Three mechanisms had been proposed: the polymer raises the glass transition temperature ($T_g$) of the mixture and so lowers mobility at the storage temperature (ref 10); it dilutes the drug and lowers its chemical potential; and specific drug–polymer interactions, such as hydrogen bonds, restrict mobility on a local scale (refs 6, 8, 11). C2 Small amounts of polymer had repeatedly been found to slow crystal growth considerably even when they barely changed $T_g$ or viscosity (refs 26–29), and drug–polymer interactions "are also considered" to decide how good an inhibitor a polymer is. C16

The exception that frames this paper comes from Yu and coworkers (Powell et al. 2013, ref 22). They added low levels of polymers with different $T_g$ to nifedipine and measured crystal growth in the glass and in the supercooled liquid. Only the polymer with the lowest $T_g$, poly(ethylene glycol) (PEG), accelerated growth; the others had little effect or slowed it, and growth rate was log-linear in polymer $T_g$. They attributed this to the segmental mobility of the polymer, "postulated" to change how easily molecules join the crystal, and argued that the effect should depend on the difference between the mobility of the polymer and that of the host. C23

The polymer studied here, PHB (poly-3-hydroxybutyrate), is a linear polyester made by many bacteria. It is semicrystalline, melts at about 175 °C and has a tensile strength of 30–35 MPa (refs 12–14). Because it is biodegradable and biocompatible, it has been studied for tissue engineering, targeted therapy and drug-delivery micro- and nanobeads (refs 15–21). In a biodegradable implant the drug may be released over months, and melt extrusion, a likely manufacturing route, tends to leave the drug amorphous, so crystallization of the drug inside the matrix "may impact" release. C3·C4 Growth rates of organic compounds had been measured with cellulose derivatives and with PVP, but PHB "does not appear" to have been studied. C5

The paper set out to fill that gap: mix several model compounds with PHB, follow crystal growth from the resulting amorphous films at several temperatures, and, after an "unexpected" acceleration appeared for some compounds, run further tests to understand it. A1·A2·A3·A4

Background concepts

Crystal growth from a supercooled liquid. A melt cooled below its melting temperature ($T_m$) without crystallizing is a supercooled liquid; below $T_g$ it becomes a glass. When a crystal nucleus forms in the supercooled liquid, it grows outward, often as a spherulite, a roughly spherical aggregate of radiating crystalline fibres. At a fixed temperature the front advances at a constant speed, so the diameter of the spherulite increases linearly with time. In this paper the growth rate is the slope of the diameter against time, in µm/sec. P3·E3·R5·R6 Many other studies report the speed of the growth front (the radius), which is half this value. X8

What sets the growth rate. The authors use a standard expression from polymer science (Hiemenz and Lodge, ref 23) as Equation 1:

Here $u$ is the crystal growth rate, $k$ a constant taken as independent of temperature, $\eta$ the viscosity of the liquid, $\Delta G$ the free energy difference between the liquid and the crystal, $R$ the gas constant and $T$ the temperature. In plain terms: growth needs both a driving force (the bracket, which grows with $\Delta G$) and molecules that can move to the crystal (the factor $1/\eta$). E1·C14

These two factors pull in opposite directions as temperature falls. Close to $T_m$ the undercooling $T_m-T$, and with it the driving force, is small while the liquid is fluid, so growth is limited by thermodynamics. Far below $T_m$ the driving force is large but the liquid becomes very viscous, and transport of molecules to the crystal limits growth. Growth rate against temperature therefore traces a bell-shaped curve (ref 24), whose maximum "typically" lies at about

In plain terms: on the low-temperature side of this maximum, any additive that changes how easily molecules move will change the growth rate; the factor 0.94 comes from ref 25. E2·C14 With the melting points of Table 1 converted to kelvin, this maximum lies at about 90 °C for FLU, 144 °C for APAP, 120 °C for ATP, 135 °C for DPB, 138 °C for CEL and 191 °C for GRI, above every growth temperature used in the paper (at most 70, 100, 60, 120, 120 and 150 °C). The authors therefore treat all their measurements as transport-limited ("is expected to be"). E2·C15·A4

Glass transition, mobility and T−Tg. $T_g$ is the temperature at which a liquid's molecular motion becomes so slow that it freezes into a glass. Above $T_g$, mobility rises steeply with temperature, so the distance $T-T_g$ is a rough measure of how mobile the liquid is. A polymer whose own $T_g$ lies below that of the compound lowers the $T_g$ of the mixture; at the same temperature the mixture is then further above its $T_g$ and more mobile. Wu et al. (ref 30) found that growth rates of polyoxyethylene with and without polymeric additives fall on one curve, "to a first approximation", when plotted against the degree of supercooling and $T-T_g$. The authors use the same idea: if growth rates of mixtures and pure compounds fall together when plotted against $T-T_g$ of each mixture, the change of $T_g$ is enough to explain the effect of the polymer. C20·P6

Growth-rate ratio. To compare compounds, the authors divide the growth rate with polymer by the growth rate without polymer at the same temperature, chosen 30–40 °C above the $T_g$ of each compound. A ratio above 1 is acceleration, below 1 retardation. E4·P7

The compounds. Six compounds were chosen to span a wide range of $T_g$: griseofulvin (GRI, $T_g$ 90 °C), celecoxib (CEL, 57 °C), (R)-(−)-3,5-dinitro-N-(1-phenylethyl)benzamide (DPB, 53 °C), acetaminophen (APAP, 21 °C), (S)-(−)-2-amino-1,1,3-triphenyl-1-propanol (ATP, 17 °C) and flutamide (FLU, −1 °C). PHB has a $T_g$ of about 0 °C and melts at 176 °C; poly(vinyl acetate) (PVAc), the second polymer, has a $T_g$ of about 40 °C. M1·M2·M3·M4·M5·M6·M7·M8

Methods in detail

The study has one experimental core, crystal growth rates measured under the microscope, supported by DSC and IR, and two analyses that turn the growth rates into an argument. The flow below follows the paper's Materials and Methods section and the Discussion.

Materials and blends

GRI, DPB, ATP, APAP and FLU came from Sigma-Aldrich and CEL was a gift from Pfizer. PHB (molecular weight 50,000) came from Advanced Polymer Materials and PVAc (molecular weight 350,000) from Scientific Polymer Products; the type of molecular-weight average is not given. M1·M2·M3·M4·M5·M6·M7·M8 Two routes were used to mix compound and polymer. GRI with 5% and 20% w/w PHB was first mixed in a mortar (500 mg powder) and then cryomilled for 10 min in a freezer mill; the same route served for PHB with CEL, APAP and FLU and for GRI with 5% PVAc. P1 DPB with 5, 10, 20 and 50% PHB was co-dissolved in a 1:1 mixture of dichloromethane and ethanol, dried by rotary evaporation and lightly ground; ATP with PHB was made "using a similar method". P2 The figures and Table 1 also show GRI with 1% PHB and FLU with 10% PHB, whose preparation the methods do not describe. X10

Growth-rate measurement

About 3 mg of blend was melted between two clean coverslips at about 5 °C above the melting point of the compound and quenched at once to room temperature. The resulting film was clear and showed no birefringence under crossed polarizers. P3·R1 The film was then heated to a set temperature on the hot stage and the growing spherulites were photographed at intervals. Diameter rose linearly with time in every run, so one slope gives the growth rate; each condition was measured three times, and the plotted error bars are standard deviations. P3·R5·R6 Temperatures went up in 10 °C steps over a range chosen for each compound: FLU 30–70 °C, ATP 40–60 °C, APAP 60–100 °C, DPB 80–120 °C, CEL 90–120 °C and GRI 110–150 °C. A4 With PHB, APAP grew two crystal morphologies; only the one that also forms without polymer was followed. R2

Note by the AI writer (not discussed in the paper): the melt step at about 5 °C above the compound's melting point lies below the melting point of PHB (176 °C) for FLU, ATP, DPB and CEL and about at it for APAP; only GRI (221 °C) was melted well above it. Whether PHB dissolved completely is supported for DPB, FLU, GRI and CEL by the IR spectra and for all mixtures by a single $T_g$, but no IR is shown for the APAP and ATP mixtures. X9

Thermal analysis and infrared spectroscopy

$T_g$ was measured by DSC on reheating at 10 °C/min after the melt had been cooled at 10 °C/min to at least 50 °C below $T_g$, and the onset value is reported. Melting points were measured at 10 °C/min on physical mixtures of the crystalline compound and the polymer, and the peak value is reported. P5 For IR, a mixture was melted between a KRS-5 window and a coverslip, quenched and scanned in transmission (128 scans, 4000–400 cm⁻¹, close to 0% relative humidity); the paper shows the NH stretching region (2800–3600 cm⁻¹) and the carbonyl region (1550–1800 cm⁻¹) for DPB, FLU, GRI and CEL mixtures (Figures 7–10). P4·R9

Two analyses

First, following Wu et al., the growth rates of DPB, GRI and CEL with PHB (and of GRI with PVAc) were replotted against $T-T_g$, using the $T_g$ of each mixture from Table 1 (Figure 11). P6·R10 Second, the ratio of growth rate with polymer to growth rate without polymer was plotted against the $T_g$ of the pure compound, for temperatures 30–40 °C above that $T_g$ (Figure 12). P7·R11 The caption of Figure 12 does not say which polymer level each point uses. X3

Experimental analysis

The same crystals, grown at different speeds

With and without polymer, the compounds crystallized as spherulites with a sharp boundary to the surrounding liquid; Figure 2 shows FLU at 40 °C and DPB at 100 °C, each without and with 5% PHB. R2 PHB therefore changes how fast the crystals grow, not what they look like. Figure 5 shows two single runs as examples. At 30 °C pure FLU reached a diameter of about 11.3 µm after 360 s, against about 6.8 µm with 5% PHB. At 120 °C pure GRI needed about 1800 s to reach about 27 µm, while with 5% PHB it reached about 53 µm in about 360 s. R5·R6 The authors summarise the GRI result as an increase "by a factor of about 10". R6·C17

PHB accelerates the three high-T_g compounds

Figure 4 gives growth rates against temperature for GRI, CEL and DPB. All series with PHB lie above the pure compounds, and the gap is largest at the lowest temperatures. R4·C7·C8

Table A. Crystal growth rates (µm/sec, mean of n = 3) of the high-T_g compounds at the lowest and highest test temperatures, read from Figure 4 (approximate); DPB with 10% PHB at 80 °C, with 20% PHB at 110 °C and GRI with PVAc at 150 °C read from the same data in Figure 11. R4

At the lowest temperatures, 5% PHB raised the growth rate about tenfold for GRI (120 °C), about sixfold for CEL (90 °C) and about fivefold for DPB (80 °C). At the highest temperatures the gain had shrunk to about 1.5-fold. R4·X5 More polymer did not always mean faster growth: for GRI at 110–130 °C the 20% blend grew fastest, but CEL grew at about the same rate with 20% as with 5% PHB at 90–100 °C and more slowly with 20% at 110–120 °C, and at 1% PHB GRI barely changed. R4.b·R4.d·R4.g·R4.h GRI with 5% PVAc grew at about the rate of pure GRI. R4.e·C9

PHB slows FLU and ATP, and barely touches APAP

Figure 3 shows the three low-T_g compounds. Here the PHB series lie at or just below the pure compounds. R3·C7

Table B. Crystal growth rates (µm/sec, mean of n = 3) of the low-T_g compounds, read from Figure 3 (approximate). R3

FLU grew at about 60% of its pure rate with 5% PHB and about 40% with 10% PHB at 30 °C; ATP at about 50–75% of its pure rate; APAP within about 75–95%. R3·X13 The results section describes these compounds as "either delayed in the presence of PHB, or was essentially the same" depending on the PHB level, and Figure 3's caption speaks of "a small reduction"; the abstract states more strongly that PHB "inhibited" them. C7·C27 For APAP the difference is close to the error bars. X13 Unlike the high-T_g compounds, the low-T_g ones show no consistent growth of the effect towards lower temperatures, although the authors write that "in general" differences were larger at lower temperatures. X5·C8

The effect follows the compound's T_g

Figure 12 condenses the growth data into one number per compound. Six unlabelled points sit at the $T_g$ values of FLU, ATP, APAP, DPB, CEL and GRI; the three low-T_g compounds lie below a ratio of 1 and the three high-T_g compounds between about 5 and 10. R11·M1·M2·M3·M4·M5·M6

Table C. Growth-rate ratios read from Figure 12 (approximate), with ratios the AI writer computed from the Figure 3 and 4 readings at 30–40 °C above each compound's T_g. R11·M1·M2·M3·M4·M5·M6·X3

The authors call this plot "very revealing": "it is clear that the polymer can accelerate or retard the crystal growth rate in a manner that depends on the Tg of the compound evaluated". In the conclusions they place the switch at a $T_g$ more than 50 °C above that of PHB. C22·C27 No compound with a $T_g$ between 21 and 53 °C was tested, so the crossover is located only within that range. M3·M5·R11

Note by the AI writer (not discussed in the paper): the paper does not state which PHB level and temperature each Figure 12 point uses. Most points match 5% PHB, but the FLU point matches the 10% PHB curve, and the DPB point matches 80 °C, which is 27 °C above the $T_g$ of DPB and outside the stated 30–40 °C window (Table C). The ordering does not change, but the exact ratios should be read as approximate. X3

What PHB does to T_g, melting point and IR spectra

Table 1 lists the $T_g$ and $T_m$ of every material and mixture. M1·M2·M3·M4·M5·M6·M7·M8·R7

Table D. Onset T_g of the materials and mixtures and peak T_m of the materials and physical mixtures, transcribed from Table 1. Figure 6 plots the same T_g values and adds DPB with 50% PHB at about 17 °C. M1·M2·M3·M4·M5·M6·M7·M8·R7·R8

Two patterns stand out. First, PHB lowers the $T_g$ of exactly the three compounds that it accelerates: GRI drops from 90 to 78 °C with 5% PHB and to 58 °C with 20%, DPB from 53 to 46 °C and CEL from 57 to 52 °C. For APAP, ATP and FLU, whose $T_g$ is close to that of PHB, $T_g$ hardly moves. R7·M1·M2·M3·M4·M5·M6 The text describes the mixture $T_g$ as "unchanged at low amounts of polymer", which fits only the three low-T_g compounds; for GRI even 1% PHB lowers $T_g$ by 5 °C. C10·X4 PVAc lowers the $T_g$ of GRI less than PHB does (84 against 78 °C at 5%). R7.b·R7.d Second, melting points shift by 0–2 °C at 1–10% polymer and by at most 4 °C at 20% (CEL, 164 to 160 °C). R7·X11

The IR spectra (Figures 7–10) show no shift of the NH bands of DPB (about 3315 cm⁻¹), FLU (about 3317 cm⁻¹) and CEL (about 3356 and 3270 cm⁻¹), and the carbonyl region of each dispersion looks like the sum of the two components. The authors conclude that "there seems to be no significant drug-polymer interaction". R9·C11 PHB itself does change: pure semicrystalline PHB has its carbonyl maximum at about 1722 cm⁻¹, while in the DPB dispersions a single band appears at about 1741 cm⁻¹, and similar bands near 1738–1743 cm⁻¹ appear with FLU, GRI and CEL. The authors read this as PHB being amorphous in the presence of the drug ("indicating"). R9·C12 (The text cites this spectral change as "Figure 6"; it is in Figure 7. Likewise the $T_g$ data are cited as "Figure 5" but appear in Figure 6. X1) In Figure 9 the two panels appear in the reverse of the caption's order. X12

Comparing at equal distance from T_g

If PHB acted only by lowering $T_g$, growth rates with and without polymer should coincide when compared at the same $T-T_g$. Figure 11 tests this for DPB, GRI and CEL. P6·R10

Table E. Growth rates near equal T − T_g of each mixture, read from Figure 11 (approximate). R10

At 5% and 10% PHB, the growth rates at equal $T-T_g$ are close to those of the pure compounds; the caption says the data "tend to collapse onto the same line". At 20% PHB, and for GRI with PVAc, growth is several times slower than the pure compound at the same $T-T_g$: "lower than would be predicted based on changes in Tg". C21·R10 The low-T_g compounds are not in this analysis (the text says Figure 11 includes ATP, but it shows CEL). X2

PVAc: a similar T_g gap without acceleration

PVAc was added as a second low-T_g polymer that is "likely" to interact only weakly with the compounds. C6 With GRI it had "little impact": about 0.13 µm/sec against 0.13 for pure GRI at 130 °C. R4.a·R4.e·C9 The $T_g$ gap between GRI and PVAc (90 against 40 °C) is about 50 °C, close to the 57 °C gap between CEL and PHB, where PHB accelerated growth about sixfold. The authors conclude: "Clearly Tg is only a crude indicator of mobility", and more sophisticated indicators "are likely to provide more mechanistic insight" into the difference between the two polymers. C26·M1·M2·M7·M8

Discussion

The authors' explanation

The authors build their explanation on Equation 1 in three steps, and then split by compound.

The authors present this as "in broad agreement with the findings and explanation given by Yu and coworkers", who linked acceleration by PEG to its high segmental mobility and argued that the effect of a polymer on the mobility of a small-molecule "solvent" should depend on the mobility difference between the two. C24·C23 In their words, "The difference in mobility between PHB and the model drugs is greatest for the high Tg compounds, leading to an acceleration of growth rate", while the retardation "most likely stems from the polymer molecules physically impeding transport of the crystallizing molecules to the crystal surface". C24·C25 They call the result "the first reported example of a polymer having compound specific inhibitory or accelerator effects on crystal growth". C29

The $T-T_g$ analysis fits this picture partly. At 5–10% PHB the growth rates of DPB, GRI and CEL collapse onto those of the pure compounds once the lowered $T_g$ is taken into account, so the acceleration at these levels is what the drop in $T_g$ predicts. At 20% PHB and with PVAc, growth is slower than the $T_g$ change predicts, which the authors leave as an observation without a separate mechanism. C21·R10

An alternative reading

Note by the AI writer (not discussed in the paper): the paper's own data allow a simpler reading of the acceleration. PHB lowers the $T_g$ of exactly the compounds it accelerates (GRI, DPB, CEL), because their $T_g$ lies far above that of PHB, and it leaves the $T_g$ of APAP, ATP and FLU unchanged, because theirs is close to it. At a fixed temperature, a lower mixture $T_g$ means a more mobile liquid, and Figure 11 shows that at 5–10% PHB the acceleration largely disappears when this is accounted for. Figure 12 plots the ratio against the $T_g$ of the pure compound, which follows the same order as the $T_g$ drop caused by PHB, so it cannot separate a plasticizing effect of PHB (lower mixture $T_g$) from the more specific mobility-difference mechanism. Neither explanation was tested by a direct measurement of mobility, viscosity or diffusion. X6·X7·R7·R10·R11

The PVAc result is the one observation that the $T_g$ gap alone does not explain: PVAc lowered the $T_g$ of GRI only to 84 °C, less than 5% PHB did (78 °C), and growth at equal $T-T_g$ was below that of pure GRI. R7.b·R7.d·R10 The authors read it as showing that $T_g$ is "only a crude indicator of mobility". C26

What it suggests for formulation

The authors state that the observations "are of importance in the context of the stabilization of organic compounds to crystallization for applications such as drug delivery", and the introduction points to PHB implants, where crystallization of a drug in the matrix "may impact" release over months. C30·C4

Note by the AI writer (not discussed in the paper): the practical message is that a polymer is not automatically a crystallization inhibitor. A soft polymer with a $T_g$ far below that of the drug can make crystals grow faster at a given temperature, and the change in mixture $T_g$ is a quick first warning. The paper covers drug-rich mixtures (up to 20% polymer for growth) above their $T_g$; polymer-rich implants, storage below $T_g$, nucleation and overall crystallization during storage were not studied, so the size of the effect in a real PHB implant is not known.

Limitations

Limits stated by the authors

The authors name one limit themselves: PVAc did not accelerate GRI although its $T_g$ gap is comparable to that of PHB and CEL, so "Clearly Tg is only a crude indicator of mobility", and "more sophisticated indicators" are "likely" needed. C26 They also note that the growth rates were taken 30–40 °C above the compound $T_g$, at large undercooling. P7·C15

The AI writer's own judgement

• Figure 12 conditions. The PHB level and temperature behind each ratio are not given; the FLU point fits 10% rather than 5% PHB and the DPB point fits 80 °C, outside the stated window. X3
• Mechanism not measured. No viscosity, molecular mobility, relaxation time or diffusion was measured; $T_g$ is the only proxy, and the mobility-difference and impeded-transport explanations remain interpretations. X7
• Plasticization as an alternative. The accelerated compounds are exactly those whose $T_g$ PHB lowers, and at 5–10% PHB most of the acceleration disappears against $T-T_g$. X6
• Weak retardation. APAP stays within about 75–95% of its pure rate, close to the error bars, and for the low-T_g compounds the effect does not grow at lower temperature as the text states in general. X13·X5
• Driving force inferred, not computed. The unchanged driving force rests on peak melting points of physical mixtures (shifts of 0–4 °C) and on the IR spectra; $\Delta G$ was not estimated. X11
• Text and figures. Two figure references are wrong (Figure 5 for the $T_g$ plot, Figure 6 for the IR change), the text names ATP in Figure 11 where the figure shows CEL, and Figure 9's panels are in reverse order. X1·X2·X12
• Incomplete methods. The preparation of GRI with 1% PHB and FLU with 10% PHB is not described, and the dispersion of PHB in the APAP and ATP films, melted below the PHB melting point, is documented only by a single $T_g$. X10·X9
• Comparability. Growth rates are slopes of diameter, twice the radial growth velocity reported in many studies. X8
• Scope. Six compounds, growth above $T_g$ only, PVAc only with GRI, and ATP and APAP at a single PHB level. A2·A3·A4

Conclusion

This short paper shows that a small amount of the same polymer can push crystal growth in opposite directions. With 5% PHB, crystals of GRI, CEL and DPB, whose $T_g$ lies 53–90 °C, grew about 5- to 10-fold faster at the lowest temperatures tested, while FLU and ATP, whose $T_g$ is close to that of PHB, grew somewhat slower and APAP barely changed. R3·R4·R11 PHB left melting points and IR bands unchanged, so the authors place its effect on mobility, and they explain the switch by the mobility difference between polymer and compound, following Yu and coworkers. C18·C19·C24·C28 The paper's own $T-T_g$ analysis shows that at 5–10% PHB the acceleration is largely what the lowered mixture $T_g$ predicts, while 20% PHB and PVAc slow growth beyond that, and the authors concede that $T_g$ is only a crude indicator of mobility. C21·R10·C26 In the AI writer's view, the result is a reminder for formulation that a low-T_g polymer can plasticize a high-T_g drug and speed its crystallization rather than slow it.