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Langmuir 2009, 25, 1970-1979
Nanoprecipitation of Polymethylmethacrylate by Solvent Shifting: 1. Boundaries Julien Aubry,† Francois Ganachaud,*,† Jean-Pierre Cohen Addad,‡ and Bernard Cabane*,§ Inge´nierie et Architectures Macromole´culaires, Institut Charles Gerhardt CNRS UMR5253, ENSCM, 8 Rue de l‘Ecole Normale, 34296 Montpellier Cedex, France, Laboratoire de Spectrome´trie Physique de Grenoble, UMR CNRS/UJF 5588, UniVersite´ Joseph Fourier Grenoble I, BP 87, 38402 Saint-Martin d’He`res Cedex, France, and Laboratoire PMMH, CNRS UMR 7636, ESPCI, 10 rue Vauquelin, 75231 Paris Cedex, France ReceiVed September 12, 2008. ReVised Manuscript ReceiVed December 11, 2008 Nanoparticles of polymethylmethacrylate (PMMA) have been produced through the solvent shifting process (also called the “Ouzo process”) in which water (nonsolvent) was added to a solution of PMMA in acetone or tetrahydrofuran (solvent). At low concentrations of PMMA in the initial solution, and for large additions of water, the process yielded PMMA nanoparticles with a narrow distribution of particle sizes. The mean particle diameter varied as a power law of the initial PMMA concentration in the solvent, in agreement with the predictions from the Smoluchowski equation for an aggregation process that has definite “start” and “stop” times. At higher PMMA concentrations, the mixing process yielded microparticles coexisting with PMMA nanoparticles. The boundary that separates the Ouzo region of compositions (PMMA nanoparticles only), from the “non-Ouzo” region (nano- and microparticles) has been determined. This boundary does not appear to have any relation to the spinodal decomposition line of the ternary solutions: the transition from Ouzo to non-Ouzo behavior must have another unknown origin.
Introduction “Solvent-shifting” is a very simple process by which hydrophobic molecules are dispersed in water as tiny (at least submicrometric) droplets or particles.1 The process appears deceptively simple: the hydrophobic solute is first dissolved into a polar solvent that is fully miscible with water, and then this solution is mixed with a large amount of water. The solution becomes a nonsolvent for the hydrophobic molecules and it phaseseparates into small droplets or particles and a continuous phase. An everyday use of this process is the spontaneous emulsification of alcoholic drinks that are diluted in water, such as Ouzo in Greece and “Pastis” in France.2-5 Industrially, the “solvent shifting” route is used to manufacture submicrometric particles of, for example, Vitamin A,6 dyes,7 and drugs.8 It has some advantages over other processes such as high-pressure homogenization or grinding, in particular the very small sizes that can be achieved (often nanometric), the simple nature of equipment, the low energy costs, and the easy implementation as an online * Corresponding author. E-mail:
[email protected]. Tel: 33 4 67 14 72 96. Fax: 33 4 67 14 72 20 (F.G.). E-mail:
[email protected]. Tel: 33 1 40 79 47 15. Fax: 33 1 40 79 45 23 (B.C.). † Institut Charles Gerhardt CNRS UMR5253, ENSCM. ‡ Universite´ Joseph Fourier Grenoble I. § CNRS UMR 7636, ESPCI. (1) For recent reviews on spontaneous emulsification by solvent shifting, see: (a) Horn, D.; Rieger, J. Angew. Chem., Int. Ed. 2001, 40, 4330–4361. (b) LopezMontilla, J. C.; Herrera-Morales, P. E.; Pandey, S.; Shah, D. O. J. Dispersion Sci. Technol. 2002, 23, 219–268. (c) Miller, C. A. Surf. Sci. Ser. 2006, 132, 107–126. (2) Sitnikova, N. L.; Sprik, R.; Wegdam, G.; Eiser, E. Langmuir 2005, 21, 7083–7089. (3) Grillo, I. Colloid Surf., A 2003, 225, 153–160. (4) Carteau, D.; Pianet, I.; Brunerie, P.; Guillemat, B.; Bassani, D. M. Langmuir 2007, 23, 3561–3565. (5) Scholten, E.; van der Linden, E.; This, H. Langmuir 2008, 24, 1701–1706. (6) Horn, D.; Schmidt, H. W.; Ditter, W.; Hartmann, H.; Lueddecke, E.; Schmieder, K. U. S. Patent 4,522,743, 1985. (7) (a) Kasai, H.; Nalwa, H. S.; Oikawa, H.; Okada, S.; Matsuda, H.; Minami, N.; Kakuta, A.; Ono, K.; Mukoh, A.; Nakanishi, H. Jpn. J. Appl. Phys., Part 2: Lett. 1992, 31, L1132-L1134. (b) Texter, J.; Travis, W. B.; Flow, V. U.S. Patent 5,624,467, 1997. (8) Violante, M. B.; Fischer, H. W. U.S. Patent 4,997,454, 1991.
process. The main drawback is the large dilution of thus-prepared dispersions or emulsions, with mass fractions as low as 10-4. The papers in this series address this issue, i.e., why nanoprecipitation is limited to such low concentrations and whether there are ways to overcome this limitation. Previous reports have already indicated that the production of metastable dispersions or emulsions is limited to a small region of the composition map, called the Ouzo region.9 When oils were used as hydrophobic solutes, ethanol as the solvent, and water as the nonsolvent, metastable emulsions were obtained only if the final mass fraction of solute was below 2 × 10-2. With organic dyes, steroids, carotenoids, or polymers, metastable dispersions of nanoparticles were likely obtained, again limited to similarly low solute concentrations.6,10-15 At present, the physical cause of this limitation is not understood. According to one school of thought, the Ouzo region is the region where the solution is sufficiently dilute to be metastable with respect to the concentration of hydrophobic solute; spontaneous fluctuations of the solute concentration produce very small nuclei of pure solute, and only those nuclei that are larger than a critical size grow by capturing other solute molecules. This nucleation-andgrowth process would produce a dispersion of pure solute droplets or particles.9 Beyond the Ouzo boundary, the solution would be unstable, and large-scale fluctuations of the solute concentration would grow spontaneously, as in spinodal decomposition processes, yielding macroscopic aggregates. In this view, the (9) Vitale, S. A.; Katz, J. L. Langmuir 2003, 19, 4105–4110. (10) Brick, M. C.; Palmer, H. J.; Whitesides, T. H. Langmuir 2003, 19, 6367– 6380. (11) (a) Van Keuren, E.; Georgieva, E.; Durst, M. J. Dispersion Sci. Technol. 2003, 24, 721–729. (b) Van Keuren, E. R. J. Dispersion Sci. Technol. 2004, 25, 547–553. (c) Van Keuren, E.; Bone, A.; Ma, C. Langmuir 2008, 24, 6079–6084. (12) Lannibois, H.; Hasmy, A.; Botet, R.; Chariol, O. A.; Cabane, B. J. Phys II 1997, 7, 319–342. (13) Stainmesse, S.; Orecchioni, A.-M.; Nakache, E.; Puisieux, F.; Fessi, H. Colloid Polym. Sci. 1995, 273, 505–511. (14) Galindo-Rodriguez, S.; Allemann, E.; Fessi, H.; Doelker, E. Pharm. Res. 2004, 21, 1428–1439. (15) Legrand, P.; Lesieur, S.; Bochot, A.; Gref, R.; Raatjes, W.; Barratt, G.; Vauthier, C. Int. J. Pharm. 2007, 344, 33–43.
10.1021/la803000e CCC: $40.75 2009 American Chemical Society Published on Web 01/26/2009
Phase Boundaries in Nanoprecipitation of PMMA
Ouzo boundary is the spinodal line of the ternary solution. Another school of thought holds the opposite point of view that interdiffusion of solvent and water always causes the solution to become unstable with respect to concentration fluctuations, and that it is through a spinodal decomposition mechanism that the solution decomposes into solute particles and the solvent mixture.10 In this case, the Ouzo boundary could be related to a modification of the spinodal decomposition process according to the solute concentration. Systematic experiments performed with a polymer as the hydrophobic solute, can provide some critical information regarding the formation of particles and the location of the Ouzo region where only nanoparticles are obtained. Indeed, the nanoprecipitation process has been largely used to generate nanoparticles or nanocapsules; for a recent review on the preparation of polymer-based colloids using the Ouzo effect, see ref 16. First, the choice of the polymer aims to prevent the growth of the nanodroplets through Ostwald ripening, or their loss through dissolution-recrystallization process, as observed when dispersing oils and dyes, respectively: it is possible to keep the polymer particles over extended periods of time. Second, the boundary of the Ouzo region has been reported to follow a simple law in the case of polymer solutes. Indeed, while Stainmesse et al.13 produced dispersions of polycaprolactone (PCL) nanoparticles through a solvent shifting process, they found that the maximum polymer concentration (boundary of the Ouzo region) decreased exponentially with the S/W ratio. This trend was confirmed in numerous other solvent-shifting experiments.14,17,18 In order to determine the nature of the processes that take place on either side of this Ouzo boundary (nucleation and growth? spinodal decomposition?), it is necessary to know the interaction free energies of the different components in the ternary system. The system polymethylmethacrylate (PMMA)/acetone or tetrahydrofuran (THF)/water has been extensively used in a related process, which is the manufacturing of porous membranes by pouring water (nonsolvent) on a concentrated polymer solution. In this case, the spinodal decomposition of the polymer solution leads to the separation of polymer-rich and water-rich domains, which become the membrane and the pores, respectively. Thanks to previous work in this field, polymer-solvent and polymernonsolvent interaction parameters are known,19-21 so that it should be possible to make quantitative prediction for the phase separation processes of the same ternary systems in the more dilute composition regions. This paper (the first in a series of three) presents the results of the solvent shifting process performed in the PMMA/acetone/ water and PMMA/THF/water systems. We show that different objects can be obtained, e.g., PMMA nanoparticles slightly swollen with solvent, or coexisting nanoparticles and large polymer lumps (referred to as “microparticles” in the rest of this paper), depending on the initial solution composition, or the amount of added water. We first determine the characteristics of the nanoparticles that are produced by nanoprecipitation, and then for each system, we determine the equilibrium phase separation boundary of the ternary solutions (binodal line) and (16) Ganachaud, F.; Katz, J. L. ChemPhysChem 2005, 6, 209–216. (17) Thioune, O.; Fessi, H.; Devissaguet, J. P.; Puisieux, F. Int. J. Pharm. 1997, 146, 233–238. (18) Murakami, H.; Kobayashi, M.; Takeuchi, H.; Kawashima, Y. Int. J. Pharm. 1999, 187, 143–152. (19) Cheng, J.-M.; Wang, D.-M.; Lin, F.-C.; Lai, J.-Y. J. Membr. Sci. 1996, 109, 93–107. (20) Lai, J.-Y.; Lin, S.-F.; Lin, F.-C.; Wang, D.-M. J. Polym. Sci., Part B 1998, 36, 607–615. (21) Schuhmacher, E.; Soldi, V.; Nunes Pires, A. T. J. Membr. Sci. 2001, 184, 187–196.
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the Ouzo boundary of the nanoprecipitation region, before finally discussing the nature of the nanoprecipitation process. In the second paper we shall discuss the influence of additives, such as surfactants, on the control of nanoprecipitation and shelf stability. In the third paper we shall use the Flory-Stockmayer theory to calculate the location of the spinodal lines of the ternary systems, and compare this location with that of the Ouzo boundary. We will then propose an alternative explanation for the nature of the Ouzo boundary, and a model for the switch from nanoprecipitation to microprecipitation.
Experimental Section Materials and Methods. PMMA was purchased from Aldrich. Size exclusion chromatography in THF yielded a weight-average molar mass of 14700 g/mol with a polymolecularity of 1.54. Acetone and THF were respectively purchased from Analar Normapur and Riedel de Haen with a purity of 99%. Brij56 or polyoxyethylene (10) cetyl ether, a nonionic surfactant of intermediate hydrophiliclipophilic balance (HLB) (12.9), was purchased from Aldrich and systematically introduced in the water to ensure long-term colloidal stability of the dispersion. NaOH pellets were purchased from SDS with a purity of 98%. High-performance liquid chromatography (HPLC)-grade water was purchased from Panreac, and buffer solutions were obtained from Carlo Erba. Unless otherwise stated, all products were used as received. Particle size analysis was performed on filtered (polyester membrane filters, pore size 1.2 µm) and undiluted dispersions using back-scattered quasi-elastic light scattering (Nanotrac 250). This apparatus uses the Brownian motion of particles in a fluid to determine particle size distributions (PSDs). The laser provides a beam of wavelength λ ) 780 nm, which is scattered by the particles so that the signal frequency is shifted according to the Doppler effect caused by their velocities. This scattered, frequency-shifted light is transmitted to the photodetector together with a part of the initial beam that is directly reflected to the photodetector without having been scattered by particles. This reflected beam has the same frequency as the original laser and acts as a reference signal for detection.22 The power spectrum of the interference signal is calculated by high-speed fast Fourier transform digital signal processor hardware and inverted to give the PSD. The fact that the signal is taken at 180° from the original beam simplifies the mathematics and makes it possible to analyze turbid, i.e., concentrated, colloidal dispersions with sizes ranging from 0.8 to 6500 nm. The Nanotrac software supplies volume and number PSDs using Lorenz-Mie theory and intensity PSDs using Rayleigh-Debye theory (see Supporting Information). For our measurements, we chose to indicate the intensity-average particle size dI because this is generally the particle size provided by other dynamic light scattering instruments. The calculation of particle sizes requires the knowledge of the viscosity and refractive index of the continuous phases, which were deduced from tables23,24 according to the water/solvent composition of the continuous phase. For each measurement we also indicated the polydispersity in particle sizes, dV/dN, where dV is the volume-average particle size and dN is the number-average particle size. The particle morphology was investigated using scanning electron microscopy (SEM). SEM samples were prepared by depositing a drop of the PMMA dispersion on an aluminum foil and letting it evaporate at room temperature. The resulting film of PMMA nanoparticles was then vacuum-coated with gold and analyzed. Centrifugation of the dispersions was carried out at an acceleration of 60 × g for 30 min using a Sorvall GLC-2B centrifuge. Nanoprecipitation Process. PMMA was first dissolved in the organic solvent by stirring the powder in the solvent for one day. The mass fraction of PMMA dissolved in the solvent ranged from 10-5 to 10-2 and 2 × 10-2 for acetone and THF solutions, respectively. (22) Plantz, P. E. ACS Symp. Ser. 1998, 103–129. (23) Noda, K.; Ohashi, M.; Ishida, K. J. Chem. Eng. Data 1982, 27, 326–328. (24) Nayak, J. N.; Aralaguppi, M. I.; Naidu, B.; Vijaya, K.; Aminabhavi, T. M. J. Chem. Eng. Data 2004, 49, 468–474.
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Figure 1. Volume fraction of acetone in the particles as a function of the volume fraction of acetone in the aqueous phase. Circles represent swelling experiments on PMMA particles (first method): initial polymer fraction f fp ) 1.1 × 10-4 (black filled circles), f fp ) 3.1 × 10-4 (black open circles), f fp ) 1.2 × 10-3 (gray filled circles), f fp ) 1.5 × 10-3 (gray open circles). Black squares are results obtained by weighing centrifuged gels after swelling (second method).
Then, the aqueous phase (water, aqueous solution of Brij56, aqueous solution of NaOH or buffer) was poured quickly into the organic solution (process 1) under moderate magnetic stirring (200 rpm). The amounts of organic solution and aqueous phase and the mass fraction of PMMA in the organic solution were chosen to reach the desired final mass fractions of PMMA and solvent in the ternary system PMMA/solvent/water. These compositions are noted as f pi (initial mass fraction of PMMA in the solvent), f fp (final mass fraction of PMMA), and fs (mass fraction of solvent in the final solution). A typical recipe was as follows: an organic solution was prepared by dissolving 0.1 g of PMMA in 100 g of acetone. An aqueous solution was prepared by dissolving 0.1 g of Brij56 in 400 g of HPLC water. Then 9 g of aqueous solution were quickly poured into 6 g of organic solution under moderate stirring (200 rpm). Stirring was stopped right after mixing, and the resulting dispersion size was determined immediately after filtration through light scattering, without removing the solvent. Solvent Partition Coefficient. All solvents do partition between water and particles during the nanoprecipitation process. Two methods were used to measure the partition coefficient of acetone between PMMA particles and water. The first one was based on the controlled swelling of a primary aqueous dispersion, previously prepared through nanoprecipitation in the Ouzo domain and solventevaporated. Small volumes of acetone were added step by step to this dispersion, while the mixture was stirred at 200 rpm for 1 min, and then the intensity-average particle size was measured through light scattering. We found that the particle diameter increased linearly with acetone content, provided that the refractive index and viscosity of the dispersion medium were corrected through the Nanotrac software (Figure S2). Since the aqueous PMMA dispersions for these experiments were quite dilute (f pf < 2 × 10-3), we assumed that acetone added to the dispersion was mainly present in the continuous phase rather than in the particles so that φSW was approximated as the volume fraction of acetone added to the dispersion. The fraction of solvent in the particles φSP was simply calculated from swollen and nonswollen particle diameters (φSP ) 1 - d03/d3; see Supporting Information for details). The partition coefficient K ) φSP/φSW was then determined by plotting φSP as a function of φSW and measuring the slope of the fitted line. Figure 1 shows this plot for four dispersions with different initial weight fractions of PMMA in water and different particle diameters. The second method consisted of preparing a dispersion outside the Ouzo range at a sufficiently high mass fraction of acetone in order to get a gel-like sediment after centrifugation. This gel was isolated, weighted, and then dried to remove acetone completely.
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Figure 2. Determination of the Ouzo boundary using filtration to remove microparticles from the dispersion of nanoparticles. Ratio of scattered intensity of filtered dispersion/scattered intensity of raw dispersions (RIS) as a function of the mass fraction of PMMA in the final solution for two PMMA/acetone/water systems (Brij 56/PMMA ) 0.1 (b) and 14 (O)).
It was weighted again to calculate the original volume fraction of acetone in gel. Three dispersions with similar initial mass fractions of PMMA in acetone (f pi ) 10-2) and mass fractions of acetone (fs ) 0.4) were tested. They differed only by the stabilizer added to the aqueous phase (one was stabilized with Brij 56 and the other two by NaOH). Two gels were extracted from each sample from which the values of φSP and φSW are reported in Figure 1 (black squares). Equilibrium Phase Separation (Binodal Line). The binodal line is the equilibrium solubility limit of the polymer in the solvent-water mixture. It was determined in two ways. The first method consisted of titrating with water a solution of PMMA in the solvent until the mixture turned milky. The composition at the binodal line was deduced from the mass of water added at the onset of turbidity. The second method consisted of adding solvent to a dispersion of PMMA nanoparticles (dI ) 100 nm) in water that was previously made by nanoprecipitation and from which the solvent had been removed by evaporation. The intensity of scattered light was then followed until this intensity dropped sharply to nearly zero, indicating that polymer chains were dissolved in the solvent-nonsolvent mixture: this composition was taken as a point of the binodal line. Ouzo Boundary. This boundary separates a region (at low initial PMMA concentration) where solvent shifting produces nanoparticles only, from another region where it produces nanoparticles and microparticles. This boundary was determined using filtration (to separate out the microparticles) and light scattering (to detect the reduction in the number of nanoparticles). Dispersions were made according to process 1 with different PMMA initial mass fractions but keeping the same mass fraction of solvent and using an aqueous phase containing a small amount of dissolved Brij 56 (mass fraction 2 × 10-4). Half of each dispersion was filtered through a polyester membrane (pore size 1.2 µm), and the raw and filtered dispersions were analyzed using the Nanotrac instrument, which provided the PSD and a “loading index” (LI). The LI value was used to calculate the total scattered light intensity IS, since both parameters are strictly proportional (see Supporting Information and Figure S1). The ratio of the intensity of filtered dispersions to the intensity of raw dispersions, noted RIS, was then plotted as a function of final mass fraction of PMMA. An example is shown in Figure 2 for two Brij 56/PMMA ratios (r ) 0.1 and r ) 14) and similar mass fractions of acetone (fs ) 0.4). As expected, RIS is constant and close to unity at low final mass fractions of PMMA, indicating that such compositions were within the Ouzo range and that all particles passed through the filters. For dispersions containing microparticles that were removed by filtration, the final polymer mass fraction was less than in the raw dispersions, and RIS decreased. The critical
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Figure 3. SEM photographs of nanoparticles of PMMA synthesized in the Ouzo domain (a) and beyond the Ouzo boundary (b). The dispersions were made by adding aqueous solutions (water and Brij 56) to solutions of PMMA in acetone. The insets show the respective PSDs of these dispersions, obtained through light scattering.
concentration at which RIS decreases corresponds to the Ouzo boundary. This boundary is a function of the final mass fraction of solvent, but it is independent of the surfactant concentration: RIS started to decrease at f pf ) 8.10-5 and at f pf ) 10-4 for Brij 56/ PMMA ratios of 0.1 (black filled circles) and 14 (hollow circles), respectively. The full Ouzo boundary was determined for solvent mass fractions ranging from fs ) 0.05 to fs ) 0.5. Mixing Processes. In order to test the effects of mixing order and kinetics, four processes were compared. As reported before, process 1 consisted of adding in one shot the aqueous phase, of largest volume, into the organic phase. This produced the fastest mixing of the two phases. Process 2 consisted in dropwise addition of the aqueous solution to the organic solution. This technique produced a regular decrease in the solubility of PMMA, resulting in near equilibrium phase separation. Process 3 consisted in dropwise addition of the organic solution to the aqueous solution. This has been the preferred way to synthesize nanoparticles by nanoprecipitation according to the literature.10,13,25,26 Process 4 was similar to 1, but part of the solvent (10% of the full amount) was introduced in the aqueous solution instead of being used in the initial PMMA solution.
Results Most solvent shifting experiments presented here were performed by adding in one shot a large volume of aqueous phase into the organic phase (process 1, see the Experimental Section). This is a robust process that yielded metastable dispersions (i.e., dispersions with colloidal stability) provided that the aqueous phase was made with extremely pure water and that it contained a surfactant, or sodium hydroxide, or both. Indeed, we found that the quality of the aqueous phase (pH and ionic strength) had a strong effect on particle sizes. Using HPLCgrade water, we obtained populations of nanoparticles with mean diameters that were reproducible to better than 3%. We first describe the sizes, morphologies, and compositions of the obtained particles (nano and microsized ones) and then specifically explain how the phase diagram was constructed. Particle Shapes and Compositions. The particles produced in different regions of the composition map were imaged by SEM. Figure 3a presents the micrographs of dispersions made with PMMA dissolved in acetone at a low polymer mass fraction, below the Ouzo boundary. In this case, the micrographs show nanoparticles only, with regular shapes and a narrow distribution of sizes. Figure 3b presents the micrographs of dispersions made (25) Yu, W.; Tabosa do Egito, E. S.; Barratt, G.; Fessi, H.; Devissaguet, J. P.; Puisieux, F. Int. J. Pharm. 1993, 89, 139–146. (26) Bouchemal, K.; Briancon, S.; Perrier, E.; Fessi, H. Int. J. Pharm. 2004, 280, 241–251.
Table 1. Initial Mass Fraction of PMMA, Mean Particle Diameter of the Initial Aqueous Dispersions of PMMA in Water, and Obtained Partition Coefficient Using the Swelling Experiments (First Method) initial mass fraction of PMMA in the aqueous dispersion
mean particle diameter of the particles in aqueous solution (nm)
partition coefficient (slope)
1.1 × 10-4 3.1 × 10-4 1.2 × 10-3 1.5 × 10-3
150 95 130 110
1.19 0.49 0.62 1.00
at a larger PMMA mass fraction, beyond the Ouzo boundary. In this case, the micrographs show both nanoparticles and much larger objects with smooth surfaces and sizes on the order of a few micrometers (see PSD obtained by light scattering in the inset of Figure 3b; note that objects above 6.4 µm are not detected by our instrument). As acetone is fully miscible with PMMA and with water, particles made through solvent shifting should contain a fraction of solvent in equilibrium with solvent in continuous phase. The partition coefficient (K) of acetone in the PMMA/acetone/water system was determined by two methods, as indicated in the Experimental Section. As this partition coefficient is a thermodynamic constant, its value should be influenced neither by the initial mass fraction of PMMA nor by the initial mean particle diameter. This is verified since all K values determined through the first method are in the range of 0.49 to 1.19 (Table 1), a rather narrow range for a partition coefficient estimate. The mean value of the partition coefficient with this method was estimated at K ) 0.82 with a standard deviation of 0.32. The second method was used to verify that K values did not depend on the nature of the stabilizer. With this method, the mean value of the partition coefficient was K ) 1.08 with a standard deviation of 0.09 (note that the value of K is overestimated, because of the remaining cosolvent weighed in the gel-like sediment before being dried). It is obvious from these results that particles made by nanopecipitation are systematically swollen by solvent (Vide infra). The total amount of solvent in particles depends on K and on the total mass fraction of solvent in the dispersion. Still, it is important to note that the relative increase in particle diameters caused by this swelling is less than 15%, therefore solvent extraction would not affect the particle size significantly. Composition Boundaries. The maps of compositions for the ternary systems are given in the representation proposed by Vitale and Katz,9 where compositions are plotted according to the final
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Figure 4. Composition boundaries for nanoprecipitation in the PMMA/ acetone/water and PMMA/THF/water ternary systems. Filled symbols: points of the equilibrium phase separation boundary (binodal curve, bold line) determined through titration and precipitation (black: from acetone; gray: from THF) and through dissolution (black triangle: acetone). Open symbols: points of the Ouzo boundary (dashed-dotted line) determined by filtration followed by measurements of the intensity of scattered light (black: acetone; gray: THF). Compositions for which different mixing processes were compared are displayed with “×” for PMMA/acetone/water and with “|” for PMMA/THF/water.
mass fraction of PMMA (horizontal axis) and the mass fraction of solvent (vertical axis) (Figure 4). The mass fraction of PMMA was so low (10-5 to 10-3) that a log scale was adopted for the x-axis. The equilibrium phase separation boundary of the ternary solutions (the binodal line) was determined either through slow water addition to a PMMA solution, or through dissolution of a previously prepared aqueous dispersion of PMMA (see the Experimental Section for procedures). In the representation using a log scale for the polymer composition, this boundary is a nearly horizontal straight line at a constant mass fraction of solvent (Figure 4). The boundary is at a lower mass fraction of solvent in the case of THF, because THF/water mixtures are better solvents than acetone/water mixtures (see paper 3 of this series). The Ouzo boundary was determined according to the result of the precipitation process. Dispersions with a PMMA mass fraction below this boundary contained nanoparticles only. Beyond the Ouzo boundary, they contained both nanoparticles and microparticles, which were stopped by the filter (pore size 1.2 µm; see SEM images Figure 3). This made it possible to determine the boundary through a measurement of the scattered light intensity (see the Experimental Section). For instance, the measurements presented in Figure 2 indicate that microparticles were produced and retained by the filter when the initial mass fraction of PMMA was 2.5 × 10-4 (corresponding to a final mass fraction of f fp ) 10-4 because the final acetone mass fraction was fs ) 0.4). This limit was roughly the same, regardless of the Brij 56/PMMA ratio, within the range studied here. An odd feature of the Ouzo boundaries (Figure 4) is their belly like curvature, which turns back to lower final mass fractions of PMMA at low fractions of solvent. However, low fractions of solvent are obtained by adding large amounts of water, so that this feature may be an effect of the dilution by water. A different representation was used by Stainmesse et al.,13 who plotted the initial rather than the final concentration of polymer (in their case PCL) at the Ouzo boundary. When the data of Figure 4 are replotted in this way, it appears that the initial mass fraction of
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Figure 5. Ouzo boundary in the alternative representation. Vertical scale: initial mass fraction of PMMA in the solvent, log scale. Horizontal scale: solvent/water ratio. Symbols: (9) PMMA/acetone/water and (b) PMMA/THF/water. The data show an exponential decay of the initial mass fraction of PMMA at the Ouzo boundary with the solvent/water ratio. The dashed line is the limit obtained by Stainmesse et al. for PCL in acetone.13
Figure 6. Composition map of the ternary system PMMA/acetone/ water according to the state of dispersions after centrifugation. Horizontal scale: final PMMA mass fraction; vertical scale: final acetone mass fraction. Black squares indicate dispersions that yield powder-like sediments, open circles are for dispersions that yield flaky sediments, and open triangles are for dispersions that yield gel-like sediment. The dashed line is the binodal line, the solid line is the centrifugation boundary, and the dotted line is the Ouzo boundary as determined by light scattering.
PMMA decreases exponentially with the solvent/water ratio (Figure 5). According to this simple law, it is the initial concentration of PMMA in the organic solvent that is relevant for the Ouzo boundary, rather than the final concentration in the ternary mixture. We also determined the Ouzo boundary through centrifugation experiments (Figure 6). When centrifugation was applied to a dispersion of nanoparticles made in the Ouzo domain, a white sediment, fully redispersable by a vortex, was collected. On the other hand, when microparticles were present besides nanoparticles (dispersion made outside the Ouzo domain), the sediment could not be redispersed. We attributed this limit to the fact that, when microparticles are present in the samples, they coalesce more easily under the pressure of the centrifugation than do
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Figure 7. Mean particle diameter (a) and polydispersity index (b) as functions of the initial mass fraction of PMMA in acetone. Each set of data is for a different final mass fraction of solvent (b 0.05, 1 0.17, 3 0.25, 9 0.3, 0 0.35, 2 0.4). Black dots represent compositions within the Ouzo domain, whereas red dots correspond to compositions that are beyond the Ouzo domain.
nanoparticles (see Discussion section). Outside of the Ouzo boundary, we also observed that, at large solvent fractions (fs > 0.35), a gel was recovered, whereas, at low solvent fractions (fs < 0.35), a white solid-like film was observed (noted as flakes in Figure 6). This difference surely originates from the glass transition, Tg, of the solvent/PMMA mixtures, which crosses the room temperature at this acetone fraction: if the room temperature is below Tg, particles aggregate but do not coalesce, whereas, above Tg, coalescence produces a gel-like sediment at the bottom of the tube. The minimum content of acetone to introduce in the formulation to soften the nanoparticles was estimated at 0.3 to 0.4 in mass fraction, a value that is close to the one theoretically calculated, i.e., 0.22 (see Supporting Information for estimated theoretical Tg’s of acetone/PMMA mixtures).27 In conclusion, centrifugation and filtration techniques give Ouzo boundaries that are quite close, meaning that the same phenomenon is observed, i.e., the generation of increasing numbers of microparticles while crossing the Ouzo boundary. Particle Sizes. The sizes of nanoparticles in the final dispersions were measured systematically using the light scattering instrument. Series of samples were prepared through the same process, with the same addition of water and surfactant (Brij 56/PMMA ratio ) 2:1) to PMMA solutions that had increasing concentrations of PMMA. For dispersions prepared in the Ouzo range of compositions, there was a single population of nanoparticles, with a narrow size distribution (see the inset of Figure 3a). In this case, we systematically measured the mean diameter of this population as a function of PMMA concentration. For dispersions prepared in the non-Ouzo range, there were two populations corresponding respectively to nanoparticles and to microparticles (inset in Figure 3b). In that case, the measurements were carried out on filtered samples in order to evaluate the mean diameter of the nanoparticle population only. Figure 7a presents the variation of the mean nanoparticle diameter with the mass fraction of PMMA in the initial solution for the PMMA/acetone/ water system. In each series, the mean diameter varied as a power law of PMMA mass fraction (i.e., a straight line in the log-log representation of Figure 7a). This trend was true regardless of (27) Besides calculation, we also tried to experimentally determine the Tg of PMMA/solvent particles as a function of the mass fraction of solvent in particles p (f s ) using thermogravimetric analysis (TGA) and differential scanning calorimetry (DSC) devices. As solvent partitioning is a thermodynamic phenomenon, analyses were carried out on simple PMMA/acetone/water mixtures, rather than on Ouzo particles, to prevent edge effects due to their small sizes. Using five PMMA/ acetone/water mixtures, we found values in a narrow range (due to the volatility of the solvent), however in fair agreement with theoretical curves (see details in Supporting Information).
Table 2. Intercept, Slope, and Best Fit Coefficient (r2) Obtained from Fitting Particle Size vs Concentration Plots (in Log-Log Scale) Starting from Acetone (Runs 1-6, Figure 7a) and THF (Runs 7-14, Figure 8) run
solvent fraction
intercept
slope
r2
1 2 3 4 5 6 7 8 9 10 11 12 13 14
0.05 0.17 0.25 0.3 0.35 0.4 0.05 0.10 0.15 0.20 0.25 0.30 0.40 0.50
625 1350 775 1650 1915 2225 1000 975 1410 895 970 780 6530 11360
0.23 0.31 0.25 0.34 0.36 0.35 0.30 0.28 0.32 0.25 0.23 0.16 0.48 0.46
0.98 0.97 0.95 0.96 0.99 0.94 0.91 0.91 0.91 0.97 0.99 0.98 0.97 0.91
whether the dispersions were prepared in the Ouzo and nonOuzo ranges. The exponents are listed in Table 2, runs 1-6. All of them but the first one are close to 1/3, indicating that the volume per particle was proportional to the concentration of PMMA in the initial solution. There was also a slow (logarithmic) rise of the polydispersity index, indicating broader size distributions at higher initial mass fractions of PMMA (Figure 7b). Figure 8a presents the variation of the mean nanoparticle diameter for the PMMA/THF/water system. In this case, there were two distinct behaviors. At large additions of water (THF mass fractions below 0.25), the behavior was the same as in the acetone system: the variation of the mean particle diameter was still a power law of the PMMA mass fraction (exponent 1/3), and there was no effect of solvent content, nor was there any effect of the Ouzo boundary. However, at small additions of water (THF mass fractions g 0.25), the diameters were much larger, and they followed a very different behavior. At low PMMA concentrations (Ouzo range), the mean diameter was independent of the initial mass fraction of PMMA, but it increased with the mass fraction of THF. At high PMMA concentrations (nonOuzo range), the diameters increased both with the initial mass fraction of PMA and with THF content. The polydispersity index also became quite large, especially so at high THF content (Figure 8b). Mixing Mode. All experiments presented so far were performed using process 1. As mentioned above, the results were reproducible and followed clear trends, provided that the quality
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Figure 8. Mean particle diameter (a) and polydispersity index (b) as functions of initial mass fraction of PMMA in THF. Each set of data is for a different final mass fraction of solvent (9 0.05, b 0.1, 2 0.15, 10.2, 0 0.25, O 0.3, 4 0.4, 3 0.5). Black dots represent compositions within the Ouzo domain, whereas red dots correspond to compositions that are beyond the Ouzo domain. Table 3. Compositions Used for the Comparison of Mixing Processes: PMMA/Acetone/Water System (Runs 15-18) and PMMA/THF/ Water System (Runs 19-22)a dI (dV/dN) run
solvent
f × 10
fs
15b 16c 17b 18b 19b 20c 21b 22b
acetone acetone acetone acetone THF THF THF THF
0.02 1 10 10 0.1 1 10 10
0.5 0.2 0.2 0.5 0.5 0.2 0.2 0.5
i p
3
f
f p
× 10
process 1
process 2
process 3
process 4
0.01 0.2 2 5 0.05 0.2 2 5
74 (1.2) 84 (1.3) 201 (1.7) 237 (1.7) 131(1.2) 76 (1.3) 186 (1.6) 272 (1.8)
116 (1.3) 207 (1.5) 648 (1.3) 916 (1.2) 183 (1.2) 219 (1.2) 633 (2.0) 1090 (2.2)
129 (1.5) 124 (1.6) 215 (1.4) 214 (1.3) 142 (1.2) 79 (1.3) 188 (1.6) 239 (1.6)
81 (1.2) 78 (1.3) 208 (1.4) 238 (1.4) 185 (1.2) 112 (1.3) 211 (1.6) 300 (1.9)
3
a i f p: initial mass fraction of polymer; fs: final fraction in solvent; f fp: final fraction in polymer; dI: mean particle diameter in intensity (in nm); dV/dN: polydispersity index. b Concentration of hydroxide sodium in the aqueous phase: c ) 10-4 mol · L-1. c Concentration of hydroxide sodium in the aqueous phase: c ) 10-5 mol · L-1.
of water was strictly controlled. However, since solvent shifting is a nonequilibrium process that starts with a nonhomogenous situation (the initial mixing), there is the possibility that variations in the mixing protocol could lead to different final results. In order to evaluate this possibility, the results of other mixing procedures (processes 1, 2, 3, and 4 described in the Experimental Section) were compared. The comparison was performed quite systematically, using two polymer concentrations in the Ouzo region and two in the non-Ouzo region, two solvent/nonsolvent ratios, and two different solvents (see Table 3 and Figure 4). In all cases, the same HPLC-grade water was used, and NaOH in two different concentrations (Table 3) was added to control the colloidal metastability (see also the next paper of this series). In both systems (acetone and THF), the processes that produced fast mixing at the final composition (processes 1, 3, and 4) gave populations of particles with similar mean diameters and similar polydispersities. Process 2 was different, as it gave much larger particles, especially so at the highest PMMA concentrations. This difference was expected, since process 2 (dropwise addition of water to the PMMA solution) causes a slow rise in the supersaturation, which must lead to heterogeneous nucleation at low supersaturation levels. In both systems (acetone and THF), the most dilute PMMA concentrations were different, since the sizes obtained through process 2 were closer to those obtained with the other processes. This was also expected, since precipitation must be much slower at these low PMMA concentrations, and therefore the initial mode of mixing may not matter.
Discussion The aim of this discussion is to determine the mechanisms by which the polymer-solvent mixture decomposes after solvent
shifting. According to the experimental results presented above, there are different ranges of composition and water addition that lead to the formation of different types of objects, e.g. nanoparticles (swollen with solvent) or microparticles (i.e., micrometric polymer lumps, also swollen with solvent). Accordingly, for each range of initial conditions, we examine what decomposition mechanisms are possible. Nanoparticle Formation at Very High Supersaturation. When large amounts of water are added to very dilute PMMA solutions, the result of solvent shifting is quite simple: the mixture decomposes to yield a single population of nanoparticles with a narrow distribution of diameters (Figure 3a). The original hypothesis put forward by Vitale and Katz9 was that the decomposition occurred through a nucleation and growth mechanism. In this mechanism, a few critical nuclei of pure solute are formed when the solution is sufficiently supersaturated, and then these nuclei grow by capturing solute molecules from the surrounding solution. The signature of the nucleation and growth mechanism is that the number of particles remains equal to the number of nuclei. At the end of growth, the mass per particle equals the solute mass concentration divided by the number concentration of particles. As the number of nuclei varies exponentially with the supersaturation, one should expect higher solute concentrations to yield a much higher number of nuclei and therefore smaller particles. Indeed, it is observed quite generally for nucleation and growth processes that higher solute concentrations yield particles that are smaller and much more numerous.28 This is contrary to the behavior observed here in the conditions of very high supersaturation. Indeed, the mean (28) Dirksen, J. A.; Ring, T. A. Chem. Eng. Sci. 1991, 46, 2389.
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diameter increases regularly with the initial concentration of PMMA (Figures 6 and 7). Moreover, the nucleation and growth model predicts that the number of nuclei should vary rapidly with solvent quality, and therefore with the concentration of nonsolvent. Consequently, the mean particle diameter ought to become smaller at higher water additions. This is also in conflict with the behavior observed here at high supersaturation. Indeed, in such conditions (water content > 0.4), the mean diameter is independent of water content. For this high supersaturation regime, an alternative is the nucleation-aggregation mechanism.28 In this mechanism, the number of nuclei is so high that that they have frequent encounters. The probability of encounters is proportional to the square of the number of particles. It is then assumed that each encounter causes aggregation of the two particles, so that the number of aggregates per unit volume, n, varies as
dn k ) - n2 dt 2
(1)
where the rate constant k has the value calculated by Smoluchowski:29-31
k)
8kBT 3η
(2)
with kB ) 1.3806 × 10-23 J · K-1 being the the Boltzman constant, T being the temperature in Kelvin, and η being the dynamic viscosity of the dispersive medium. In a first approximation, the rate constant k can be taken as being independent of particle size.29 Equation 1 can then be integrated to yield the variation with time of the number of particles:
1 1 k k ) + t≈ t n n0 2 2
(3)
The number of aggregates can be written as a function of the mass fraction of solvent (fs), the initial mass fraction of PMMA in solvent (fpi), the densities of the dispersive medium (Fsol) and of the particles (Fp), and the mean particle diameter (d). This yields eq 4 (see detailed calculations in Supporting Information).
n)
6fsf piFsol Fpπd3
(4)
Combining eqs 3 and 4 gives the variation of d3 as a function of aggregation time t:
d3 )
8kBTFsol fs f pi ×t π Fpη
(5)
f pf, f pi, and fs are linked by the following equation:
f pf ≈ f pi fs
(6) 3
Introducing eq 6 in eq 5 leads to the final expression of d :
d3 )
8kBTFsol f f t ) 1.037 × 10-20R(fs)fpft πFpη p
(7)
The rate coefficient R(fs) contains parameters that depend solely on fs: variations of Fsol and η with fs are deduced from literature tables (represented in Figure S2),23,24 whereas Fp is deduced from φSP, which is also a function of fs (see Figure S3). For the (29) Evans, D. F., Wennerstro¨m, H. The Colloidal Domain; Wiley-VCH: New York, 1994. (30) Broide, M. L.; Cohen, R. J. Phys. ReV. Lett. 1990, 64, 2026. (31) Debenedetti, P. Metastable Liquids; Princeton University Press: Princeton, NJ, 1996.
Figure 9. Mean particle diameter as a function of the final mass fraction of PMMA. Symbols are experimental data, and lines are theoretical fits according to a nucleation-aggregation particle formation mechanism. Each set of data is for a different final mass fraction of acetone (b 0.05, 1 0.17, 3 0.25, 9 0.3, 0 0.35, 2 0.4). The contour of the symbols and the color of the lines correspond to acetone mass fraction (pink for fs ) 0.05, green for fs ) 0.3, and blue for fs ) 0.4). The color inside the symbols is black if the compositions are within the Ouzo domain and red if they are outside.
PMMA/acetone/water system, R(fs) is well determined on the range studied (0.05 < fs < 0.4) (Table 4). Thus, if the recombination goes on for a set time t, the volume per particle will be proportional to the final polymer mass fraction f pf, and the particle radius will be proportional to the cube root of this mass fraction. This is the case for our experiments (Figures 7 and 8). Moreover, plotting diameter as a function of f pf or fpi produces the same slope. This analysis assumes that all particles recombine at the same rate and grow to the same mass, as in a hierarchical process where the PSD is perfectly monodisperse; in the more general case, the diffusion limited cluster aggregation (DLCA) model30 shows that the smaller particles recombine more frequently than the larger ones, so that the final size distribution is still monopopulated, as observed in the experiments (see Figure 3). The time t during which aggregation takes place will be constant if the aggregation process has a definite start time and a definite stop time. The start time is the time at which the primary particles are formed. At very low PMMA concentrations, the mixing of solvent and nonsolvent is faster than the encounter time of macromolecules. With large additions of water, the net interaction free energy of macromolecules in this solvent mixture is quite high, much higher than thermal energies. Hence aggregation starts right after mixing, and the start time is the mixing time, provided that mixing is performed through a one-shot process. The stop time is the time at which the particles stop aggregating. This will occur through the adsorption of species that cause the particles to repel each other. Earlier work by Lannibois et al.12 demonstrated that surfactants can be used for that purpose. In the present work, we have also used the addition of OH- ions to achieve colloidal stability. Thus the stop time is the time at which adsorption of surfactant or potential determining ions occurs. A quantitative comparison of predictions of the theoretical model provided by eq 7 with experimental results is presented in Figure 9, which shows plots of particle diameter d versus f pf. For the sake of clarity, only three linear fits are represented, with a slope of 1/3. The comparison of experimental data with the predictions makes it possible to determine for each mass fraction of solvent the aggregation stop time t, as shown in Table 4. We
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Table 4. Values of the Rate Constant r(fs) and of the Aggregation Stop Time t Determined from the Fits of Experimental Data (Figure 9) to Eq 7 mass fraction of acetone fs
R(fs)
aggregation stop time t (sec)
0.05 0.17 0.25 0.3 0.35 0.4
868.0 724.7 674.0 659.0 657.1 670.5
2.75 2.93 1.34 1.76 1.58 2.49
find that the aggregation stop time is nearly independent of the mass fraction of acetone, since its values fluctuate around an average value of 2.1 s with a standard deviation of 0.6 s. The discrepancy between theoretical predictions and experimental data at low solvent fraction (fs ) 0.05) may originate from the diluting effect of water, which supposedly affects both the rate and frequency of particle encounters. The comparison with the predictions of the nucleationaggregation model was also carried out for the PMMA/THF/ water system with fs < 0.2. In this case also, good correlations were found when fitting the mean particle diameter dI by a power law of f pi with exponent 1/3. However the partition coefficient of THF in water and PMMA was not determined, so the value of φSP as a function of fs is not known. Consequently, it was not possible to calculate the aggregation stop time. Growth of Larger Particles at Low Supersaturation. When smaller amounts of water were added to a PMMA/THF solution, the particles were much larger and more polydisperse in size (Figure 8, THF mass fraction > 0.25). Moreover, the variations of their mean diameter were opposite to those described above. Indeed, the mean diameter became independent of the PMMA concentration fpi, but it increased with the THF content. In terms of numbers of particles, this indicated that there were fewer particles and that their number was determined by the supersaturation of the final solution. This behavior is no longer compatible with the nucleation-aggregation model described above. On the other hand, it matches the predictions of the nucleation-and-growth model mentioned previously.31 Indeed, when the THF content is high, the PMMA/THF/water solution has a high metastability, and it can evolve only through nucleation of PMMA particles that are larger than the critical nucleus size. At high THF contents, nucleation events are rare, and therefore these particles are far apart; consequently, they do not encounter each other. Instead, they evolve by collecting isolated PMMA macromolecules. Their growth must stop when they have collected all the available macromolecules (i.e., all the dissolved PMMA in excess of the solubility limit). Hence, the number of critical nuclei determines the final particle size. If the THF content is higher, the supersaturation is less, nucleation is more difficult, a smaller number of nuclei will be formed, and the resulting particles will be larger, as observed (Figure 7). The final size was also found to be approximately independent of the initial PMMA concentration. This is because of a compensation of two effects: when there is more PMMA, the supersaturation is higher, which yields more nuclei, but there is also more PMMA to feed the growth of these nuclei. FormationofMicroparticlesatHighPMMAConcentrations. At high polymer concentrations, beyond the Ouzo boundary, solvent shifting produced microparticles in addition to nanoparticles. Vitale and Katz proposed that this change to a larger length scale could result from a crossover to a regime in which it decomposes through spinodal decomposition. Indeed, spinodal decomposition involves small concentration fluctuations over large scales, whereas classical nucleation involves large con-
Figure 10. Thermodynamic boundaries for the system PMMA/acetone/ water. The bold black and green lines are calculated binodal and spinodal lines, respectively, using the Flory-Stockmayer theory of polymer solutions with the following interaction parameters: χPMMA/water ) 2.34, χPMMA/acetone ) 0.13, and χacetone/water ) 0.95. The black symbols are the points of the equilibrium phase separation boundary, determined in the present work for (9) the PMMA used throughout the paper (Mn ) 14 700 g · mol-1, Mw/Mn ) 1.54); (2) a very monodisperse PMMA of similar molar mass (Mn ) 14 920 g · mol-1, Mw/Mn ) 1.03); ([) a higher molar mass PMMA (Mn ) 56 500 g · mol-1, Mw/Mn ) 1.78), and (b) a large molar mass monodisperse PMMA (Mn ) 140 000 g · mol-1 and Mw/Mn )1.13), the corresponding points of which were determined by Lai et al.20 The thin lines are the dilution pathways followed by the ternary solutions during solvent shifting experiments. The red squares are the points of the Ouzo boundary determined for the PMMA described in this study and best fitted by the bold red line. Solvent shifting processes that end within this boundary (i.e., at lower polymer concentrations) yield dispersions of nanoparticles. Solvent shifting processes that end above this boundary (i.e., at higher polymer concentrations) yield mixtures of nanoparticles and microparticles.
centration fluctuations of very small scales. Thus, large-scale fluctuations in PMMA concentrations would grow spontaneously and give rise to the microparticles: indeed, the volume of polymer solution that yields a microparticle is rather large (on the order of a few micrometers according to SEM images; see Figure 3b). However, the Ouzo boundary shown in Figure 4 has the wrong slope for a spinodal line: it goes to higher polymer concentrations when the solvent quality gets worse. Still, in order to conclude on this point, it is necessary to determine the spinodal line of the ternary solutions. We have calculated the spinodal line of the PMMA/acetone/water system, and Karlstro¨m calculated the binodal line, using the Flory-Stockmayer theory of polymer solutions.32 The interaction parameters for PMMA were taken from literature values, χPMMA/water ) 2.3420 and χPMMA/acetone ) 0.13, and the best fitting of literature experimental data20 led to χacetone/water ) 0.95 (detailed calculations will be presented in the third paper of this series). Figure 10 presents the calculated binodal and spinodal lines, together with the dilution pathways that are followed by the ternary solution during mixing. The binodal line matches quite satisfactorily the experimental points determined in the present work, whatever the molar mass and/or polydispersity of the PMMA chains (see Figure 10 caption for details), and also the points determined by Lai et al.,20 hence the choice of interaction parameters is correct. The spinodal line is quite close to the binodal at high polymer concentrations, but not at the very low polymer concentrations explored in the present work. The dilution lines cross this large region that is between the binodal line and the spinodal line, where the dilute solutions are (32) (a) Thuresson, K.; Karlstro¨m, G.; Lindman, B. J. Phys. Chem. 1995, 99, 3823. (b) Piculell, L.; Lindman, B.; Karlstro¨m, G. Surf. Sci. Ser. 1998, 77, 65– 141.
Phase Boundaries in Nanoprecipitation of PMMA
metastable, but they never enter the region below the spinodal line, where the solutions would become thermodynamically unstable. Hence, a spinodal decomposition process is ruled out. The transition from Ouzo to non-Ouzo behavior must therefore have another origin. Since the polymer concentration in the ternary solution remains much lower than the spinodal decomposition boundary, the early steps of decomposition must still go through a nucleation step, followed by aggregation of the nuclei if the supersaturation is high enough. Therefore the system must still produce a population of nanoparticles during the early stages of decomposition. The final state still contains numerous nanoparticles, coexisting with a few microparticles. This could be caused by a mechanism in which the larger particles would be able to coalesce, while the smaller ones would escape coalescence. Such behavior is not that predicted by the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory for solid particles,33 although it has been observed in the case of emulsions.34 Indeed, when two droplets stabilized by surfactant collide, they deform and for a while remain separated by a flat surfactant/water/surfactant film. Then the probability of coalescence is the probability that a localized event such as a loss of surfactant35 or a curvature inversion36 will take place somewhere in the surfactant film that separates the droplets. This probability is proportional to the area of the film, and therefore to the square of the droplet radius. It has been shown that, as a consequence of this mechanism, emulsion droplets that are larger than a critical size coalesce very rapidly.34 In common emulsions, this critical size depends on the nature of the surfactant film; in the present case, it would depend on the solvent content of the ternary solutions, since that determines the adsorption or surfactant molecules or potential determining ions. Thus, the formation of microparticles in a population of nanoparticles that are swollen with solvent could result from coalescence events that take place when the largest particles of the population encounter each other, but do not take place during collisions of the smaller particles of the population. The Ouzo boundary would then correspond (33) Vervey, E. J. W.; Overbeek, J. T. G. Theory of the Stability of Lyophilic Colloids; Elsevier: New York, 1948. (34) Sonneville, O. Biliquid foams Ph.D. Thesis, University Paris VI, 1997. (35) Exerowa, D.; Kashchiev, D.; Platikanov, D. AdV. Colloid Interface Sci. 1992, 40, 201. (36) Kabalnov, A.; Wennerstrom, H. Langmuir 1996, 12, 276.
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to the polymer concentration beyond which such “larger” particles are produced and become susceptible to coalescence.
Conclusion Nanoparticle formation through solvent shifting results from a dilution of the solute molecules in a bad solvent (water), causing the nucleation of very small aggregates of solute molecules, followed by aggregation of these nuclei (nucleation-aggregation mechanism). This aggregation process has a start time (the dilution time) and a stop time (the onset of colloidal stability, due to the adsorption of ions or surfactant molecules). Consequently, the final size reached by the nanoparticles at the end of aggregation varies as a power law of the solute concentration, as predicted by the Smoluchowski kinetic model. The population of nanoparticles has a narrow size distribution, as in all aggregation processes that follow the DLCA mechanism. This mechanism requires large additions of nonsolvent (water) to the initial polymer solution. At smaller additions of water, the nucleation barrier is high, the nuclei are larger and less numerous, and they grow through the capture of nonaggregated solute molecules (nucleationand-growth mechanism). Both mechanisms yield dispersions of particles that are swollen with solvent, and have colloidal stability through adsorption of surfactants or potential determining ions. Both mechanisms are limited to very small solute concentrations, otherwise the solvent-swollen particles become large enough to coalesce and yield a secondary population of much larger microparticles. Acknowledgment. It is a pleasure for us to thank Gunnar Karlstro¨m for the application of the Flory-Stockmayer theory to the calculation of the binodal line of the PMMA/acetone/ water solutions. J.A. thanks the Languedoc Roussillon region and the CNRS for his Ph.D. grant, Dr. Abdellatif Manseri for DSC measurements, and Kevin Roger for providing some of the data for Figure 10. Supporting Information Available: Detailed information on the Ouzo boundary as determined by the Nanotrac apparatus, particle swelling, and derived relevant parameters; the experimental and theoretical evolution of acetone-swollen PMMA glass transition as a function of the mass fraction of acetone in PMMA; and the nucleation and aggregation detailed theory. This material is available free of charge via the Internet at http://pubs.acs.org. LA803000E
