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Langmuir 2006, 22, 906-910
Articles Amorphous Drug Nanosuspensions. 1. Inhibition of Ostwald Ripening Lennart Lindfors,*,† Pia Skantze,† Urban Skantze,† Mikael Rasmusson,‡ Anna Zackrisson,†,‡ and Ulf Olsson§ Pharmaceutical and Analytical R & D, Experimental Formulations, AstraZeneca R&D Mo¨lndal, SE-431 83 Mo¨lndal, Sweden, and Physical Chemistry 1, Lund UniVersity, Box 124, SE-221 00 Lund, Sweden ReceiVed August 30, 2005. In Final Form: NoVember 1, 2005 Amorphous drug nanosuspensions are prone to particle growth due to Ostwald ripening. By incorporating a second component of extremely low aqueous solubility, Ostwald ripening can be inhibited. These studies indicate that to inhibit ripening, the drug/inhibitor mixture (in the particles) must form a single phase. The drug/inhibitor mixture can be characterized by the interaction parameter χ using the Bragg-Williams theory, in which single phase mixtures are obtained for χ < 2. The χ parameter can be calculated from the (crystalline) solubility of the drug in the inhibitor, provided the inhibitor is a liquid, and the melting entropy and temperature of the drug.
1. Introduction A significant proportion of drugs on the market are poorly soluble in water, and it is expected that this will be even more pronounced in the future.1 Formulations of poorly water-soluble compounds offer a challenge to the formulation scientist, from the early discovery phase through the development to the launch of the pharmaceutical product. During the discovery phase, new compounds are evaluated by both in vitro and in vivo studies, in which liquid formulations are used most often. Poorly soluble compounds can be formulated, e.g., as aqueous pH-shifted solutions, provided the molecules are ionizable, in mixtures of water and organic cosolvents or by solubilization in cyclodextrin or micellar systems.2 With the exception of the pH-shifted aqueous solutions, significant amounts of additives are often needed to increase the solubility into the millimolar range, required for most animal studies, which may induce unwanted side effects. An interesting alternative to these formulations is aqueous nanosuspensions with typical particle sizes of the order of 100 nm. Nanosuspensions can be either crystalline3 or amorphous.4 To obtain an amorphous nanosuspension, the drug is first dissolved in an organic water-miscible solvent, and the resulting solution is then rapidly mixed with an aqueous stabilizer solution. The mechanism of particle formation by precipitation after a solvent quench has been studied in several recent papers.5-7 * Corresponding author. Telephone: +46 31 7761000. Fax: +46 31 7763834. E-mail:
[email protected]. † AstraZeneca R&D Mo ¨ lndal. ‡ Present address: Department of Chemistry, Physical Chemistry, Go ¨ teborg University, SE-412 96 Go¨teborg, Sweden. § Lund University. (1) Lipinski, C. J. Pharmacol. Toxicol. Methods 2000, 44, 235. (2) Yalkowsky, S. H. Solubility and Solubilization in Aqueous Media; Oxford University Press: New York, 1990. (3) Merisko-Liversidge, E.; Liversidge, G. G.; Cooper, E. R. Eur. J. Pharm. Sci. 2003, 18, 113. (4) Gassman, P.; List, M.; Schweitzer, A.; Sucker, H. Eur. J. Biopharm. 1994, 40, 64. (5) Lannibois, H.; Hasmy, A.; Botet, R.; Chariol, B.; Cabane, B. J. Phys. II 1997, 7, 319. (6) Vitale, S. A.; Katz, J. L. Langmuir 2003, 19, 4105. (7) Brick, M. C.; Palmer, H. J.; Whitesides, T. H. Langmuir 2003, 19, 6367.
After precipitation the organic solvent can be removed, e.g., by dialysis. However, directly after mixing the amount of organic solvent is typically between 1 and 10% (v/v). This, in combination with the amorphous state of the drug, leads to a rather high bulk concentration (apparent amorphous solubility) in such systems, and particle growth by Ostwald ripening becomes significant in many cases of practical interest. Ostwald ripening is a process where the difference in (local) solubility with particle size leads to a transport of material from small to larger particles, with an accompanying increase in the mean particle size with time.8,9 Higuchi and Misra10 showed that it is possible to inhibit the Ostwald ripening process in o/w emulsions by incorporating a small amount of a second component with a very low aqueous solubility, and this has been explained theoretically by Kabalnov et al.11 Briefly, the incorporation of a second component with low aqueous solubility leads to a difference in composition between large and small particles during the Ostwald ripening process. This difference may counterbalance the driving force for Ostwald ripening and eventually result in a termination. This paper concerns Ostwald ripening and its inhibition for amorphous nanosuspensions of different drug substances. Here we also address the requirement that the inhibitor and the main component are miscible and demonstrate that when these two components do not mix (in the particles) inhibition of the ripening is not obtained. 2. Experimental Section 2.1. Materials. Nifedipine was purchased from Sigma, whereas felodipine, bicalutamide, C1, C2, and C3 were obtained from AstraZeneca. All drug structures are shown in Figure 1. N,NDimethylacetamide, DMA (Aldrich), sodium dodecyl sulfate, SDS (Millchem UK Ltd), poly(vinylpyrrolidone) K30, PVP (BASF), Miglyol 812N (Hu¨ls, an approximately 60/40 (w/w) mixture of C8 and C10 triglycerides), and 1-decanol (Aldrich) were used as received. (8) Ostwald, W. Z Phys. Chem. 1900, 34, 495. (9) A. S. Kabalnov, E. D. Shukin, AdV. Colloid Interface Sci. 1992, 38, 69. (10) Higuchi, W. I.; Misra J. J. Pharm. Sci. 1962, 35, 581. (11) Kabalnov, A. S.; Pertzov, A. V.; Shukin, E. D. Colloids Surf. 1987, 24, 19.
10.1021/la0523661 CCC: $33.50 © 2006 American Chemical Society Published on Web 12/21/2005
1. Inhibition of Ostwald Ripening
Figure 1. Molecular structures of the drug compounds chosen for this study. 2.2. Preparation of Amorphous Nanosuspensions. Amorphous nanosuspensions of the drug compounds were prepared by rapidly injecting a drug solution (typically 100 mM drug dissolved in DMA) into an aqueous stabilizer solution in a vial placed on an ultrasonic bath (Elma Transsonic Bath T460/H). Typically 0.01 mL of the DMA solution was injected into 0.99 mL of stabilizer solution, resulting in a 100-fold dilution of the drug compounds. Hence, the final drug concentration in such a nanosuspension was 1 mM. For one compound, nifedipine, however, a five times higher concentration was used, i.e., a final concentration of 5 mM. Furthermore, in the NMR studies (see below), a final drug concentration of 10 mM was used. The stabilizer solutions contained 0.2% (w/w) PVP and 0.25 mM SDS in all cases except for the bicalutamide nanosuspension and during the NMR studies, where SDS was omitted. Ostwald ripening inhibitors used were Miglyol and a Miglyol/decanol 1:1 (w/w) mixture. The drug/inhibitor ratio was in most cases 4:1 (w/w), although for felodipine/Miglyol different ratios were studied as well. 2.3. Size Measurements. The average particle size of the suspensions was monitored as a function of time by fiber optic quasi-elastic light scattering (FOQELS, Brookhaven Instruments Corporation) and the particle sizes reported are averages computed by the second cumulant method. 2.4. Solubility Measurements. The solubility of drugs in Miglyol and in a Miglyol/1-decanol 1:1 (w/w) mixture was determined by adding an excess of the drug to typically 1 mL of the inhibitor. The mixture was allowed to equilibrate using magnetic stirring for 48 h at room temperature (∼23 °C) and was then passed through a 0.2 µm hydrophilic PTFE filter. The concentration was determined by UV-HPLC. 2.5. Differential Scanning Calorimetry Measurements. The melting temperature, Tm, and enthalpy of melting, ∆Hm, were determined by differential scanning calorimetry (DSC) analysis on samples of crystalline drug material using a Mettler-Toledo DSC 820 in an open vial configuration and a scanning speed of 10 K/min. The entropy of melting, ∆Sm, was calculated as ∆Sm ) ∆Hm/Tm. 2.6. NMR Studies. 1H NMR spectra were obtained on a Bruker DRX 800, operating at 800 MHz, at a temperature of 22 °C in a deuterated solvent mixture, 1:9 (v/v) N,N-dimethyl acetamide-d9/ D2O.
3. Results and Discussion Amorphous nanoparticles of the different drug substances were prepared by a rapid solvent quench method as described in section 2.2. The fact that the particles obtained with this preparation technique were amorphous in contrast to crystalline was concluded from cryo transmission electron microscopy experiments and by measuring the drug solubility in water using the particle
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Figure 2. The cube of the mean particle diameter, 〈d〉3, in amorphous nanosuspensions of felodipine (1 mM) vs time, for no added Miglyol (2), 20:1 drug/Miglyol (w/w) (4), 10:1 drug/Miglyol (w/w) (b) and 4:1 drug/Miglyol (w/w) (O).
suspensions. The amorphous solubility of these compounds are in general an order of magnitude or more higher than their crystalline solubility.12 Immediately after preparation, the colloidal stability of the suspensions was investigated by time-resolved dynamic light scattering experiments. Figure 2 shows the time evolution of the particle size in suspensions of felodipine with different drug/ inhibitor ratios. The data are plotted as the cube of the average particle diameter, 〈d〉3, versus time, because in the case of Ostwald ripening the average volume of the particles is expected to grow linearly with time. The initial particle size is approximately 100 nm, in all of the cases. In the absence of inhibitor, a significant coarsening of the particle suspension was observed. After 1 h, the average particle diameter has grown to 350 nm. For a drug/ Miglyol ratio of 20:1, a coarsening is still observed, but the coarsening rate is reduced by approximately a factor of 2 compared to the case without inhibitor. For drug/Miglyol ratios of either 10:1 or 4:1, the coarsening is completely inhibited and no particle growth is observed. At long times the drug is prone to crystallization. This however, will be discussed in a forthcoming publication. In the classical theory of Liftshitz and Slyozov13 and Wagner14 (LSW), the Ostwald ripening rate can be written as 2 d〈d〉3 64γVm c∞D ) dt 9RT
(1)
Here, γ is the interfacial tension, Vm is the molar volume of the dispersed compound, c∞ is its bulk solubility (i.e., the molecular concentration that is in thermal equilibrium with a macroscopic bulk phase), and D is the diffusion coefficient in the solvent. Finally, R is the gas constant and T the absolute temperature. For felodipine, Vm ) 300 cm3/mol, c∞ ≈ 25 µM12 and the diffusion coefficient can be estimated to 5 × 10-10 m2/s from the molecular weight. From the data in Figure 2 for the felodipine particles without Miglyol we obtain the Ostwald ripening rate d〈d〉3/dt ) (12) Lindfors, L.; Forsse´n, S.; Hedberg, P.; Skantze, U.; Zackrisson, A.; Olsson, U. Langmuir 2006, 22, 911. (13) Lifshitz, I. M.; Slyozov, V. V. Zh. Eksp. Teor. Fiz. 1958, 35, 479. (SoV. Phys. JETP 1959, 35, 331). (14) Wagner, C. Z. Electrochem. 1961, 35, 581.
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solubility in the solvent of the dispersed phase, due to the interfacial energy, which decreases with increasing particle size. Hence, large particles have a lower solubility than small ones. In a polydisperse system, the bulk will at steady state have a concentration which is intermediate between the different solubilities. The bulk is therefore supersaturated with respect to large particles while being below the solubility for small particles. As a result, large particles grow and small ones dissolve, and the mean particle size increases with time. The radius dependence of the solubility is obtained from the Kelvin equation16
{ }
c(r) ) c∞ exp
2γVm rRT
(2)
where r is the particle radius and c∞ is, as above, the solubility for a macroscopic phase corresponding to a particle with infinite radius. The radius dependence of the solubility is related to the radius dependence of the molar chemical potential
Figure 3. Cube of the mean particle diameter, 〈d〉3, in amorphous nanosuspensions of C2 (1 mM) vs time, for 4:1 drug/Miglyol (w/w) (b) and 8:1:1 drug/Miglyol/decanol (w/w) (O).
1.2 × 104 nm3/s. The interfacial tension is unknown, but from the experimentally determined ripening rate and the molecular parameters listed above, we obtain with eq 1 the value γ ≈ 4 mN/m. This value is significantly lower than the typical value for a water-alkane interface, which is 50 mN/m. Hence, one would expect from eq 1 a ripening rate that is 1 order of magnitude higher than that observed experimentally. The presence of SDS and PVP as stabilizers may complicate the situation with regards to the effective interfacial tension. However, there is another possible reason for the low experimental ripening rate. In the LSW model, the molecular exchange kinetics is assumed to be diffusion controlled. It may well be that surface integration is here a time consuming step in the process of molecular exchange, as has been discussed extensively in the context of, e.g., crystal growth.15 Another source for a reduced ripening rate could be a reduced diffusion coefficient in the vicinity of the interface if PVP forms a dense layer surrounding the particles. We hope to return to the problem of the absolute ripening rate in a forthcoming publication. For some compounds, Miglyol alone did not inhibit Ostwald ripening. However, in some of those cases, an equal weight mixture of Miglyol-decanol mixture did inhibit Ostwald ripening. Figure 3 shows for the compound C2 the time evolution of 〈d〉3 for two different particle compositions. For a drug/Miglyol ratio of 4:1, inhibition of the ripening is not obtained. However, when the inhibitor is a 1:1 mixture of Miglyol and decanol, a drug/ inhibitor ratio of 4:1 is sufficient to prevent a ripening of the particles. With the results of Figures 2 and 3, we have demonstrated that (i) Ostwald ripening of amorphous nanoparticles can be inhibited by mixing in a second, essentially water insoluble, component; however, (ii) one cannot use simply any water insoluble compound as seen by the fact that Miglyol may inhibit the ripening of one drug compound but not another. Higuchi and Misra10 were the first to demonstrate that Ostwald ripening can be inhibited by adding small amounts of a second insoluble compound to emulsion droplets, and the ripening of composite droplets was later analyzed by Kabalnov et al.11 The origin of the Ostwald ripening process is that there is an excess (15) Nielsen, A. G. Croat. Chem. Acta 1980, 53, 255.
µ(r) ) µ0 +
2γVm r
(3)
and eq 2 is obtained as the monomer concentration that is in thermal equilibrium with a particle of radius r, i.e., µ(r) - µ0 ) RT ln{c(r)/c∞}. Mixing in a second component results, if the two components are miscible, in a decrease of the chemical potential due to the entropy of mixing. Denoting the major component (i.e., the drug) and the second component as “1” and “2”, respectively, we have for the major component
µ1(r) ) µ01 +
2γVm + RT ln{1 - x2} r
(4)
assuming ideal mixing. Here x2 is the mole fraction of the second component in the particle. In the case that the second component is insoluble in the continuous solvent, a ripening process leads to a decrease of x2 in the growing particles, whereas x2 increases in particles that shrink. If the distribution of the second component is initially uniform, i.e., the same x2 value in all of the particles, this may eventually lead to a termination of the ripening process where a small radius and high x2 balances a large radius and small x2 so that the chemical potential and hence the solubility is the same for the different radii. One requirement being that the average x2 value is sufficiently high. Based on eq 4, this scenario has been discussed in detail by Kabalnov et al.11 To account for the fact that Miglyol does not inhibit the ripening of particles for all of the different drug components, we also need to consider interactions. Equation 4 assumes ideal mixing and neglects contributions to the chemical potential from intermolecular interactions. A simple model accounting for intermolecular interactions is the Bragg-Williams model of regular solutions where the interactions are characterized by what is commonly referred to as a χ parameter, whereas one still assumes ideal mixing for the entropy term.16 Within the BraggWilliams model, eq 4 is modified to
µ1(r) ) µ01 +
2γVm + RTχx22 + RT ln{1 - x2} r
(5)
In the Bragg-Williams model the components are miscible at all compositions for χ < 2 (χ varies with temperature as 1/T) as µ1 decreases monotonically with x2 in the whole composition range, (16) Evans, D. F.; Wennerstro¨m, H. The Colloidal Domain: Where Physics, Chemistry, Biology and Technology Meet, 2nd ed.; VCH Publishers Inc.: New York, 1994.
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Table 1. Summary of the Calculated and Observed Results on the Inhibition of Ostwald Ripening in Amorphous Nanosuspensions Using a Ratio of 4:1 Drug/Inhibitor (w/w)a drug compound
inhibitor
S (mM)
χ
inhibitionc (yes/no)
felodipine nifedipine bicalutamide C1 C1 C2 C2 C3 C3
Miglyol Miglyol Miglyol Miglyol Miglyol/decanolb Miglyol Miglyol/decanolb Miglyol Miglyol/decanolb
69 8.9 1.4 0.65 9.8 2.2 37 1.8 5.5
0.4 1.2 1.4 2.7 0.7 2.8 0.6 3.2 2.8
yes yes yes no yes no yes no no
µ01 - µ01c ) (∆Sm - ∆Cp)(Tm - T) + T∆Cp ln{Tm/T}
(7)
where ∆Sm is the entropy of melting at Tm and ∆Cp is the heat capacity difference between the liquid and the crystal, and we have also used ∆Hm ) Tm∆Sm. As originally suggested by Hildebrand17 (for a more recent discussion see ref 18), ∆Sm ≈ ∆Cp. With this approximation, eq 7 is simplified into µ01 - µ01c ) T∆Sm ln{Tm/T}, and inserted into eq 6, we obtain
a
The Bragg-Williams chi parameter, χ, has been calculated according to eq 8 using measured values of the crystalline solubility, S, of drug in inhibitor and the melting entropy and temperature of the crystalline material. b 1:1 mixture (w/w). c Particle growth was measured using dynamic light scattering (FOQELS) at 1.0 mM drug in 1% (v/v) DMA (aq), except for nifedipine which was studied at 5 mM in 5% DMA (v/v).
0 e x2 e 1. For χ > 2 on the other hand there is a miscibility gap and µ1 is a nonmonotonic function of x2. When it comes to the mechanism of ripening inhibition, it is clear that as long as µ1 is a monotonically decreasing function of x2, inhibition may still be obtained. In other words, inhibition is expected when χ < 2. Inhibition may also be obtained if χ is only slightly larger than 2. The basic requirement for termination of the ripening is that µ1 relaxes to the same constant value in all of the particles. If this can be achieved without having such a high concentration of the second component in the smallest particles that phase separation occurs, inhibition can be obtained. However, if there is phase separation within the particles, one does not expect inhibition. In a phase separated binary system, the chemical potential (here we refer to the last two terms on the right-hand side of eq 5) remains constant when the average concentration is varied, and the inhibition mechanim is therefore lost. The χ parameter can be estimated from experimental data of the melting of the crystalline drug and the solubility of the crystalline drug in the inhibitor. The standard chemical potential, µ01, appearing in eqs 3-5 refers to the pure amorphous reference state. The corresponding chemical potential in the crystalline state we denote µ01c. At equilibrium, the chemical potentials in coexisting phases are equal, and if we consider the solubility of the crystalline drug in the inhibitor, we have at equilibrium µ1 ) µ01c. At equilibrium, the solution chemical potential is given by µ1 ) µ01 + RT(χ(1 - xsc)2 + ln{xsc}), where xsc is the equilibrium solubility of the crystalline drug in the inhibitor. From the condition µ1 ) µ01c, we then obtain
µ01 - µ01c + ln{xsc} RT χ)(1 - xsc)2
enthalpy and entropy changes for the different steps, and assuming that the heat capacities are temperature independent, we obtain
(6)
The crystalline solubility in the inhibitor was measured for the different drug-inhibitor combinations and the results are summarized in Table 1. What now remains is to estimate the chemical potential difference between the (supercooled) amorphous state and the crystalline state at the temperature T < Tm, where Tm is the melting temperature of the crystal. To do that, we consider a heating-cooling cycle where the crystal first is heated to Tm, then it melts at that temperature, and finally the liquid is supercooled back to the temperature T. Summing up the
∆Sm ln{Tm/T} + ln{xsc} R χ)(1 - xsc)2
(8)
Tm and ∆Hm were measured in DSC experiments. From the calorimetry and solubility data, χ parameters were calculated according to eq 8, for the various drug-inhibitor pairs, and the results are all summarized in Table 1. In the case where decanol and Miglyol were used together as an inhibitor mixture, they were treated, for simplicity, as a pseudosingle component. In Table 1, we also report on whether Ostwald ripening inhibition was observed experimentally. The inhibition efficiency and the estimated χ parameters are compared for nine different systems. In five of these, inhibition was observed, whereas in the remaining four it was not. In all systems where inhibition was observed χ < 2, and in all systems where inhibition was not obtained χ > 2. Despite the assumptions involved, we thus find a strong correlation with the first order rule that inhibition of Ostwald ripening is only effective when the inhibitor is completely miscible with the main component. We note, however, that for none of the systems investigated we obtain a χ parameter really close to 2, and hence the accuracy of the approximate model is difficult to estimate. Within the Bragg-Williams model, phase separation at x2 ) 0.1 occurs for χ ) 2.7 and at x2 ) 0.2 for χ ) 2.3. For a drug/inhibitor weight ratio of 4:1, x2 ≈ 0.15-0.25 for the different drugs. Hence for the large χ parameters, we may be far into the predicted miscibility gap. It should be pointed out that for the compound C3 neither Miglyol nor a Miglyol/decanol mixture did inhibit Ostwald ripening, in agreement with the Bragg-Williams theory (χ > 2). To further investigate the state of mixing of drug and inhibitor within the particles, we have conducted high resolution 1H NMR experiments on some of the particle suspensions. In these experiments, the particles were formulated without the surfactant SDS because the resonances from the surfactant would overlap with the majority of the Miglyol resonances. The polymer PVP was kept as the only stabilizer. The ideas behind these experiments are as follows. The transverse relaxation rate and hence width of the proton resonances depends on the rate of molecular reorientation.19 If Miglyol is present in a fluid domain (as would be expected if the drug and Miglyol do not mix but form separate domains), the relevant correlation time is given by the tumbling of individual Miglyol molecules in a fluid Miglyol rich environment. This correlation time is expected to be of the order of 10-9 s, and the resonances from Miglyol are expected to appear as narrow peaks in the spectrum. If Miglyol on the other hand forms a composite amorphous solid together with the drug, (17) Hildebrand, J. H.; Prausnitz, J. M.; Scott, R. L. Regular and Related Solutions; Van Nostrand Reinhold Co.: New York, 1970. (18) Neau, S. H.; Bhandarkar, S. V.; Hellmuth, E. H. Pharm. Res. 1997, 14, 601. (19) Abragam, A. The Principles of Nuclear Magnetism; Oxford University Press: London, 1961.
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Figure 4. NMR spectra for (a) a Miglyol emulsion, (b) an amorphous nanosuspension of felodipine (10 mM) with 4:1 (w/w) drug/Miglyol, and (c) an amorphous nanosuspension of C1 (10 mM) with 4:1 (w/w) drug/Miglyol.
where the molecular dynamics is essentially frozen, or at least slowed significantly, the relevant reorientational correlation time becomes that associated with the rotational diffusion of the particle. This correlation time is given by
τt )
πηd3 6kBT
(9)
where η is the viscosity of the solvent (≈ 0.9 mPas for water) and kB is the Boltzmann constant. For particles with a diameter of 100 nm in water, the correlation time becomes of the order of 10 µs, which is the same order of magnitude or longer than the inverse of typical dipolar interactions (measured in Hz). The NMR spectrum should then not be in motional narrowing but consist of very broad lines (hundreds of kHz) with static dipolar splittings or at least in the slow motion regime. In practice, this means that the NMR signal is effectively absent in the highresolution spectrum. In Figure 4a, we present, as a reference, the NMR spectrum recorded for a drug free emulsion of Miglyol. The methyl (-CH3) and main methylene (-CH2-) resonances are clearly observed together with the R and β methylene resonances of the fatty acid residues, consistent with the fluid character of the emulsion drops. In Figure 4b, we show the spectrum recorded from nanoparticles composed of felodipine and Miglyol with a drug/Miglyol ratio of 4:1. Here the Miglyol resonances, as well as the resonances from the drug felodipine, are absent demonstrating that Miglyol forms a composite amorphous solid together with the drug. Note that this result also demonstrates that the particles are truly amorphous. If the drug would have crystallized, it would not have mixed with Miglyol and the Miglyol resonances would have been observed in the spectrum.
The NMR spectrum in Figure 4b also contains another piece of information. The amorphous solubility of felodipine at the present particle composition is approximately 25 µM.12 This concentration is above the detection limit, but still no resonances from felodipine is observed. Note also that spin relaxation in the monomer state is expected to be slow, which would result in narrow resonances from a pure monomer state. The fact that no signal at all is observed means that the molecular exchange between the monomer state and the amorphous state in the particles is rapid compared to the experimental time scale which here would be defined as the inverse bandwidth of the amorphous state which may be as broad as 106 Hz. Hence, the average lifetime of monomeric felodipine may be shorter than 10-6 s, before the molecule is adsorbed by a particle. As a reasonable upper limit, one can say that the lifetime is at least shorter than 10-4 s. As was presented in Table 1, the compound C1 could not be stabilized against Ostwald ripening by Miglyol alone, and χ ) 2.7 was estimated from the model calculations indicating that the drug and Miglyol do not form a homogeneous mixture. That this is indeed the case is shown by the NMR spectrum in Figure 4c. Here, the formulation consists of a C1/Miglyol ratio of 4:1. The resonances from Miglyol are present in the spectrum, demonstrating a low viscous fluid environment for the Miglyol molecules, whereas no resonances are observed from the drug compound (for example one would expect the N-methyl resonances to appear at 2.5-3 ppm). This result demonstrates that C1 and Miglyol do not form a homogeneous mixture, in accordance with the model calculations, and which explains why inhibition of Ostwald ripening fails for this case.
4. Conclusions We have investigated the inhibition of Ostwald ripening of amorphous nanoparticles by the method of adding a second component to the particles that is essentially insoluble in the continuous solvent. The main conclusions of the present paper can be summarized as follows. Inhibition is obtained when the drug and the inhibitor form a homogeneous composite mixture in the amorphous particles. However, when phase separation between the drug and inhibitor occurs, Ostwald ripening is not inhibited. NMR spectroscopy is a convenient method to investigate whether the drug and the inhibitor are homogeneously mixed in the particles. The Bragg-Williams model of regular solutions was used to predict the miscibility of drug and inhibitor and hence the inhibition efficiency. For the nine different systems investigated here, the predictions from the model calculations were consistent with the experimental observations. Acknowledgment. We are grateful to Per-Olof Eriksson at AstraZeneca R&D Mo¨lndal for carrying out the NMR measurements. U.O. acknowledges financial support from the Swedish Research Council (VR). LA0523661
