Formation of Colloidal Dispersions of Organic Materials in Aqueous

Langmuir 2003, 19, 6367-6380

6367

Formation of Colloidal Dispersions of Organic Materials in Aqueous Media by Solvent Shifting† M. Christine Brick,*,‡,§ Harvey J. Palmer,| and Thomas H. Whitesides‡ Imaging Materials and Media, Eastman Kodak Company, Rochester, New York 14650-1731, Department of Chemical Engineering, University of Rochester, Rochester, New York 14627, and Kate Gleason College of Engineering, Rochester Institute of Technology, Rochester, New York 14623 Received January 31, 2003 This paper describes the preparation of colloidal dispersions of water-insoluble organic materials by a “solvent-shifting” procedure, in which a concentrated solution of an organic solute in a water-miscible organic solvent is dispersed into a large volume of aqueous (nonsolvent) bulk solution containing colloidal stabilizers. In the majority of cases studied, the solute separates as 0.1-0.5 µm amorphous particles. The particle size is strongly correlated with the local supersaturation, i.e., the ratio of the solute feed concentration to the instantaneous value of the equilibrium solubility in the bulk, and also shows a weak dependence on the solute feed concentration. The results obtained on systematic variation of the precipitation conditions, including the amount of organic solvent in the aqueous phase, the solute feed concentration, and the mixing conditions, are discussed in terms of a mechanism of particle formation comprising dispersion of the feed solution as small droplets, followed by solvent/water counterdiffusion at the interface. Rapidly decreasing solvent quality, resulting from this interdiffusion, leads to local liquid-liquid phase separation by spinodal decomposition. This mechanism is shown to be consistent with the preferential formation of noncrystalline (amorphous) particles and with the observed changes in particle size and formation rate.

Introduction Many applications exist that require a uniform dispersion of sub-micrometer particles in a fluid or gel phase. Examples include photographic emulsions, specialty coatings, and sustained-release, drug-delivery systems. A common method for producing such dispersions is to synthesize the desired material, precipitate it in pure form as large crystals, reduce the crystals to the desired particle size by a combination of energy-intensive methods, such as grinding and ball milling, and then disperse the resultant particles into the desired fluid medium. The disadvantages of this approach include high energy consumption, long processing times, contamination and degradation of the material from the grinding and milling processes, the difficulty of producing particles that are smaller than a micrometer, and a limited ability to control the size distribution of the resultant particles. Consequently, it is desirable to develop an alternative method for producing colloidal dispersions of sub-micrometer particles directly following the material’s synthesis. One such method is by direct precipitation. A common method used to precipitate an organic solid from solution is to add a nonsolvent such as water. If the water has appreciable solubility in the organic solution, its presence typically will reduce the solubility of the organic solute, thereby creating supersaturated conditions and ultimately the formation of a precipitate. Solvent shifting is widely used both in the laboratory and in industrial practice for obtaining filterable crystalline precipitates as part of a purification procedure. To obtain an easily filterable product (i.e., a relatively large particle size) and to exclude impurities, the nonsolvent is slowly * To whom all correspondence should be addressed. E-mail address: [email protected]. † Part of the Langmuir special issue dedicated to David O’Brien. ‡ Eastman Kodak Company. § University of Rochester. | Rochester Institue of Technology.

added to a solution of the compound being purified. The relatively low degrees of supersaturation achieved in this manner lead to slow heterogeneous nucleation, followed by growth of these nuclei into large, well-formed crystalline particles. The purpose of the current investigation is to determine if the solvent-shifting concept can be adapted and exploited in a controlled fashion to produce dispersions of sub-micrometer sized particles of organic materials in water. The key to producing sub-micrometer particles by solvent shifting is to create conditions that favor very rapid particle formation and little or no particle growth. In the current work, these conditions are created by rapidly dispersing into a bulk aqueous phase a concentrated solution of the organic solute in a water-miscible organic solvent. Because the organic solvent is soluble in water, a single bulk liquid phase is maintained throughout the experiment. However, because the organic solute is highly insoluble in water, the blending of the organic solution with the aqueous phase creates a highly supersaturated condition that favors rapid precipitation of the organic solute. With adequate mixing, and in the presence of appropriate colloidal stabilizers in the aqueous phase (in this work, a mixture of poly(vinylpyrrolidone) (PVP) and sodium dodecyl sulfate (SDS)), we demonstrate that stable colloidal suspensions of the organic solute can routinely be obtained. There have been several previous efforts to apply the solvent-shifting technique to make colloidal dispersions of sub-micrometer sized particles. LaMer and Dinegar produced monodisperse colloidal dispersions of sulfur with mean sizes of 0.3-0.4 µm by precipitating sulfur from ethanol and acetone solutions through the careful addition of water.1 The solvent-shifting technique has been used to precipitate small particles of photographic couplers,2βcarotenoids,3,4 the lipid-lowering drug probucol,5 and a variety of other water-insoluble drugs.6-8 A recurring (1) LaMer, V. K.; Dinegar, R. H. J. Am. Chem. Soc. 1950, 72, 4847. (2) Godowsky, L.; Duane, J. J. U.S. Patent 2,870,012, 1959.

10.1021/la034173o CCC: $25.00 © 2003 American Chemical Society Published on Web 05/14/2003

6368

Langmuir, Vol. 19, No. 16, 2003

Brick et al.

theme in these studies is the formation of particles of amorphous (noncrystalline) material. In addition, in pharmaceutical applications, the precipitating compound often tends to separate as a liquid phase.9,10 The only study that has investigated the role of process conditions on the characteristics of the organic particles formed by solvent shifting is that by Gutoff and Swank, who prepared colloidal dispersions of organic dyes by adding water and stabilizers to a solution of the dye in a water-miscible, volatile organic solvent.11 They observed that the mean particle size increased with decreasing amounts of water added and with increasing time between precipitation and solvent removal, suggesting that physical ripening (i.e., growth of large particles at the expense of small particles) had a significant effect on particle size. The particles formed by their procedure also were amorphous, rather than crystalline, and were of the order of 1 µm or less. In the current study, the use of the solvent-shifting technique to produce colloidal dispersions of sub-micrometer sized organic particles is examined in greater depth. In particular, we quantitatively assess the impact of the following process conditions on the size and morphology of the particles produced by solvent shifting: the solute concentration in the organic feed solution, the choice of the organic solvent, the concentration of the organic solvent in the aqueous phase, the feed rate of the organic solution to the aqueous phase, and the intensity of mixing. On the basis of these experimental results, a mechanism of particle formation during solvent shifting at high levels of supersaturation is formulated and discussed. Theoretical Concepts Supersaturation. A supersaturated solution is one in which the concentration of the solute in solution exceeds its thermodynamic solubility limit. The free energy of such a system can thus be lowered by spontaneous formation of a second phase in equilibrium with a more dilute (saturated) solution. The differential change in the Gibbs free energy that accompanies this process is

dG ) (µ1* - µ1) dn1 ) -RgT ln

( ) a1 a1*

( )

γ1x1 dn1 ) -RgT ln dn1 (1) γ1*x1* where µ1 and µ1* are the chemical potentials of the solute in the supersaturated solution and saturated solution, respectively, Rg is the gas constant, T is absolute temperature, a1 is the activity of the solute, x1 is the mole fraction of the solute in solution, γ1 is its activity coefficient in solution, n1 is the number of moles of solute exchanged (3) Auweter, H.; Andre´, V.; Horn, D.; Lu¨ddcke, E. J. Dispersion Sci. Technol. 1998, 19, 163. (4) Horn, D.; Lu¨ddcke, E. In Fine Particles Science and Technologys From Micro to Nanoparticles; Pelizzetti, E., Ed.; NATO Advanced Science Institutes Series 3; Kulwer Academic Publishers: Dordrecht, 1996; Vol. 12, p 761. (5) Frank, S.; Lo¨froth, J. E.; Bostanian, L. U.S. Patent 5,780,062, 1998. (6) Violante, M. R.; Steigbigel, R. T.; U.S. Patent 4,783,484, 1988. (7) Violante, M. R.; Fischer, H. W. U.S. Patent 4,826,689, 1989. (8) Violante, M. R.; Fischer, H. W. U.S. Patent 4,997,454, 1991. (9) Kirwan, D. J.; Orella, C. J. In Handbook of Industrial Crystallization; Myerson, A. S., Ed.; Butterworth Heinemann: New York, 1993; Chapter 11. (10) Midler, M., Jr.; Paul, E. L.; Whittington, E. F.; Mauricio, F. W.; Liu, P. D.; Hsu, J.; Pan, S.-H. U.S. Patent 5,314,506, 1994. (11) Gutoff, E. B.; Swank, T. F. Design, Control, and Analysis of Crystallization Processes; AICHE Symp. Ser., No. 193; American Institute of Chemical Engineers: New York, 1980; p 43.

between the two phases, and the asterisk distinguishes the conditions for the saturated solution from those of the supersaturated state. The ratio of the activity of the solute in the supersaturated solution to that at equilibrium is commonly referred to as the supersaturation, S

S)

(

)

a1 γ1x1 (µ1 - µ1*) ) ) exp a1* γ1*x1* RgT

(2)

The supersaturation is a measure of the driving force for crystallization.12 For most circumstances, it is sufficient to assume that γ1 ≈ γ1*, so that S = (x1/x1*). Amorphous Phase Solubility. In the experiments described in this paper, as well as those of others,7,8 the organic solutes separate as an amorphous phase. Therefore, it is more appropriate to compute the supersaturation S using the solubility of the amorphous, rather than the crystalline, phase. From a thermodynamic viewpoint, the amorphous state is unstable, relative to the crystalline state, at temperatures below the melting point of the crystal. This means that the free energy, and consequently the solubility, of the amorphous state is higher than that of the crystalline phase. The solubility of the amorphous phase at the temperature of the experiments may be estimated by assuming that the amorphous state is equivalent to a supercooled liquid solution of the solute. The calculation involves the consideration of a thermodynamic path that involves (1) raising a mole of amorphous material from the operating temperature T to the melting point of the crystal TM, (2) allowing the resultant liquid phase to crystallize, and (3) lowering the temperature of the crystalline phase to T. Because dG ˆ ) dH ˆ - TdS ˆ , the free energy change for this three-step process is computed from the associated changes in enthalpy H ˆ and entropy S ˆ 13

∆H ˆ )

∫TT

C ˆ P(A) dT - ∆H ˆM+

∫TT

C ˆ P(C) dT

∆S ˆ )

∫T

C ˆ P(A) dT - ∆S ˆM + T

∫T

C ˆ P(C) dT T

M

TM

M

T M

where ∆H ˆ M is the molar enthalpy of melting, ∆S ˆ M is the molar entropy of melting, and C ˆ P(A) and C ˆ P(C) are the molar heat capacities of the amorphous and crystalline states, respectively. Because ∆G ˆ ) 0 for the crystallization process (step 2), ∆S ˆ M ) (∆H ˆ M/TM). In addition, we assume that the heat capacities are independent of temperature to obtain

(

∆G ˆ ) -∆H ˆM 1-

)

T + (C ˆ P(A) - C ˆ P(C))[(TM - T) TM T ln(TM/T)] (3)

However, according to eq 1, the change in the Gibbs free energy that accompanies the phase transition of 1 mol of solute from the amorphous to the crystalline state is

∆G ˆ ) µcrystalline* - µamorphous* ) - RgT ln

(

)

xamorphous* xcrystalline*

(4) (12) Mullin, J. W. Crystallization: Butterworth-Heinemann Ltd.: Oxford, 1993; Chapter 13. (13) Sandler, S. I. Chemical and Engineering Thermodynamics; John Wiley: New York, 1989; Chapter 8.

Colloidal Dispersions by Solvent Shifting

Langmuir, Vol. 19, No. 16, 2003 6369

Table 1. Thermodynamic Properties of the Organic Solutes Used in This Studya ID

MW

∆H ˆ M, kJ/mol

TM, °C

ratio of solubilities (amorphous:crystalline)

D-1 B-1 D-2 C-1

398 261 365 721

32.6 29.8 53.3 45.1-59.7

155 150 263 >224

44 29 9700 1100-10000

The solubility ratio is computed with eq 5. C-1 decomposes prior to completion of the melt transition; thus, only a range of values for its heat of melting and solubility ratio can be provided.

assuming that the activity coefficient for the solute in solution at the two concentration levels is the same. If we combine eqs 3 and 4 and assume that the difference in the molar heat capacities is small (in particular, ∆C ˆ P(TM - T) , ∆H ˆ M), we obtain the following result

[

∆H ˆM (1 - T/TM) RgT

]

(

J ) An exp

a

xamorphous* ) xcrystalline* exp

occur. For either homogeneous or heterogeneous nucleation, the rate of nuclei formation per unit volume J is a strong function of the degree of supersaturation S and is expected to be governed by15

(5)

If the concentration of the solute is less than the solubility of either the amorphous or the crystalline material, no phase separation can occur. For a solute concentration greater than the equilibrium solubility of the crystalline phase, and less than the solubility of the amorphous state, only the crystalline phase can form. For higher solute concentrations, the formation of either the amorphous or the crystalline state is thermodynamically possible, and the phase that actually forms will be a reflection of the kinetics and mechanism of the phaseseparation process. According to eq 5, the larger the heat of melting and/or the higher the melting point of the crystalline solid, the larger the effective solubility of the amorphous, relative to the crystalline, phase. Table 1 presents the values of these two properties, together with the ratio of the solubilities of the amorphous and crystalline states from eq 5, for the four solutes investigated in this study. Clearly, the compounds D-2 and C-1 are distinguished by heats of melting and melting point temperatures that are nearly 2-fold larger than those for D-1 and B-1. Consequently, the solubility ratio (amorphous to crystalline) for D-2 and C-1 is over 100-fold larger than that for D-1 and B-1. Thus, D-2 and C-1 have a substantially larger concentration range within which only crystalline phase separation is possible. Classical Nucleation. Although supersaturation with respect to the crystalline phase is a necessary condition for crystallization, it is not sufficient to guarantee the rapid appearance of crystals. Before crystals can develop, nucleation must occur, i.e., nuclei (seeds) must form to act as centers for rapid crystal growth. In a solution containing no impurities, an increase in the degree of supersaturation will increase the probability that a cluster of molecules of sufficient size will form and act as a nucleus for crystal growth. Ample experience has revealed that such pristine conditions are extremely difficult to achieve in practice. However, when they are approached, very high degrees of supersaturation are required to initiate the nucleation process. Nucleation under these conditions is called homogeneous nucleation.14 Under normal laboratory conditions, because of the presence of impurities that act as nucleation sites (e.g., dust particles), heterogeneous nucleation will inevitably (14) Ny´velt, J.; So¨hne1, O.; Matuchova, M.; Broul, M. The Kinetics of Industrial Crystallization; Elsevier: New York, 1985; Chapter 3.

)

-16σ3Y2b 3k3T3(ln S)2

(6)

where σ is the interfacial free energy of the critical nucleus, Y is the molecular volume, and k is Boltzmann’s constant. For heterogeneous nucleation, the prefactor An is related to the number of heterogeneous nucleation sites, and b is a factor accounting for the diminished surface area for a heterogeneous nucleus. For homogeneous nucleation, An derives from the molecular collision frequency and equals 1033 nuclei s-1 mL-1 and b ) 1. Amorphous Phase Separation by Spinodal Decomposition. The formation of a crystalline phase by a nucleation-and-growth mechanism is subject to a variety of kinetic barriers. Liquid-liquid phase separation can occur faster than crystallization, particularly for complex molecules for which entropic constraints can substantially decrease the rate of crystal formation. At low supersaturations, liquid-liquid phase separation occurs by a nucleation-and-growth mechanism, just as it does for solid-liquid phase separation. At sufficiently high supersaturations, the separation of phases is better described by the process of spinodal decomposition, the rate of which is controlled by the diffusional growth of concentration fluctuations in the solution.16-18 The criterion for stability of a homogeneous solution is shown schematically in Figure 1, which is a plot of the free energy of mixing ∆Gmix vs solute mole fraction x, taken from Lupis.19 If the curve is concave upward (as in Figure 1a), the free energy of the homogeneous solution (point C) is always less than a combination of two phases (A and B) of equivalent aggregate composition; therefore the single-phase solution is always the stable state. Conversely, if the plot of ∆Gmix vs x is concave downward (Figure 1b), the solution is thermodynamically unstable with respect to the growth of fluctuations in the concentration of solute.19 If a solution is brought very rapidly from a condition described by Figure 1a to one described by Figure 1b, this growth of solute concentration fluctuations (spinodal decomposition) will lead to the formation of a second phase. The condition described in Figure 1c is the transition between the two regimes and is a point on the spinodal of the system. Such a transition from a stable to an unstable state can be brought about by a rapid change in temperature or, in our system, by a rapid change in the solvent composition. As will be discussed later, the precipitation process in our experiments is believed to begin with the creation and dispersion of tiny droplets of the solute-solvent mixture within the aqueous phase. The counterdiffusion of water and organic solvent in these droplets creates the conditions presented in Figure 1b to initiate the spinodal decomposition process. Experimental Section Chemical Components. Most of the work in this study was carried out using the yellow cyanophenyl furanone dye (D-1). Several other solutes were also investigated. All of the solute (15) Myerson, A. S.; Ginde, R. In Handbook of Industrial Crystallization; Myerson, A. S., Ed.; Butterworth Heinemann: New York, 1993; Chapter 2. (16) Cahn, J. W. Acta Metall. 1961, 9, 795. (17) Cahn, J. W.; Hilliard, J. E. J. Chem. Phys. 1958, 28, 258. (18) Cahn, J. W.; Hilliard, J. E. J. Chem. Phys. 1959, 31, 688. (19) Lupis, C. H. P. Chemical Thermodynamics of Materials; Prentice Hall: Englewood Cliffs, NJ, 1983; Chapter 3.

6370


Brick et al.

Figure 1. Free energy of mixing vs composition for a homogeneous solution. Point C represents the composition and free energy of mixing of a homogeneous solution. M is the composite of phases A and B into which it is considered to separate. In the stable case (left-hand figure), all concentration fluctuations are energetically unfavorable; in the unstable case, all are energetically favorable; and at the spinodal point, sufficiently small fluctuations are isoenergetic (from Lupis19). Table 2. Organic Solvents Used in the Precipitation Experimentsa solvent

mol wt

bp, °C (at 1 atm)

log P

N-methylpyrrolidinone (NMP) acetonitrile (ACN) methyl sulfoxide (DMSO) dimethylacetamide (DMA) methanol (MeOH)

99.1 41.1 78.1 87.1 32.0

202.0 81.6 189.0 165.0 64.5

-0.73 -0.39 -1.38 -0.77 -0.76

a log(P) is the octanol/water partition coefficient whose values were obtained from the literature as cited.20-22

Figure 2. Molecular structure of the organic solutes chosen for this study. structures are shown in Figure 2; they include a second yellow dye (D-2), a photographic coupler (C-1), and a substituted benzophenone (B-1). These materials were chosen in part because of their thermodynamic melting properties (determined by differential scanning calorimetry). As shown in Table 1, D-1 and B-1 have similar melting temperatures and molar enthalpies of melting (around 150 °C and 30 kJ/mol), as do D-2 and C-1 (around 240 °C and 50 kJ/mol). As discussed in the previous section, these differences produce substantial variations in the relative solubilities of the amorphous and crystalline forms of these species, such that solutes D-2 and C-1, having a larger concentration range within only the crystalline phase can precipitate, compared to solutes D-1 and B-1. Moreover within each pair, there is a substantial difference in structural complexity and molecular weight, which should affect the speed of formation of the highly ordered crystalline phase. The organic solvents used in the study, together with some of their properties,20-22 are given in Table 2. The solvents were chosen because they are miscible with water and are good solvents for a variety of organic materials, including those in Table 1. Most of the batch precipitation work was done using N(20) Medchem, (property estimation program, v. 3.54), Medicinal Chemistry Project, Ponoma College, Claremont, CA. (21) Hansch, C.; Anderson, S. J. Org. Chem. 32, 2538, 1967. (22) Hansch, C.; Leo, A. Substituent Constants for Correlation Analysis in Chemistry and Biology; John Wiley: New York, 1979.

Figure 3. Schematic diagram of the precipitation batch reactor. methylpyrrolidone (NMP). All solutions were filtered through a 10-µm stainless steel filter to remove insoluble contaminants. The solute concentration in each solution was confirmed by highpressure liquid chromatography (HPLC). The dispersion stabilizer used in the aqueous phase for all the precipitation experiments was comprised of a mixture of 0.03% (1 mM) sodium dodecyl sulfate (Eastman Chemical Company, used without further purification) and 0.5% poly(vinylpyrrolidone) (Luviskol K30 from BASF, MW ∼60K). The aqueous phase for the batch precipitations was prepared using high-purity water and was filtered through a 1-µm polycarbonate filter. The dispersant concentration was confirmed by microwave solids analysis. Batch Precipitator. A schematic of the batch precipitator constructed for this investigation is shown in Figure 3. The precipitation reactor was a stainless steel jacketed beaker with a maximum volume of 1 L. Batch sizes ranged from 300 to 400 g. The temperatures of the solute feed and aqueous solutions were each controlled to 30 ( 0.1 °C. The contents of the reactor were mixed with one of several impellers driven by a compressed air turbine fitted with a stainless steel shaft. Impeller speeds were varied between 50 and 400 revolutions/min, with 200


Figure 4. Detail of the interaction chamber of the highpressure mixer. The dotted arrows are intended to indicate the nature of the fluid flows during operation. The drawing is not to scale. revolutions/min used in most experiments. The organic solution containing the solute was fed to the reactor at a steady rate (generally 0.5 g/s) with a high-precision metering pump that delivered the solution through an inlet in close proximity to the impeller. The location of the inlet was chosen to ensure rapid, complete dispersion of the solution within the aqueous phase. The results were found to be relatively insensitive to stirrer speed, the choice of the mixing device, and the precise location of the injection point, as long as it was close to the impeller. A 4 cm diameter, flat-blade turbine impeller was used for most experiments. The reactor cover held the mixing head, pH probe, resistive thermal detector temperature probe, an optical probe connected via a fiber optic cable to a colorimeter to detect the presence of solute in the solution, and two stainless steel hollow ports through which the solute solution could be fed, either near the top or near the bottom of the mixing head. The feed-flow rate, solute solution temperature, and reactor solution temperature were computer controlled using a LabVIEW program that also directed continuous measurement and recording of the reactor solution pH, mixer speed, and optical density of the reactor solution during the batch precipitation experiment. A typical experiment consisted of delivering the organic solute solution at a fixed flow rate to the aqueous solution at the mixer head and extracting dispersion samples at discrete time intervals during the feed solution delivery period. The extracted samples were immediately quenched by 1:10 dilution with ultrapure water (to prevent ripening), and the particle size was measured using dynamic light scattering (see below). Control experiments showed that the dispersion particle size was stable after quenching for at least 1 h. High-Pressure Mixer. Experiments with the batch reactor showed that mixing intensity over the range available in that device had little effect on the particle-formation rate. On the basis of our preferred mechanism for particle formation, we expected that the independence of particle formation rate on mixing would fail at both substantially higher and lower mixing intensities. To achieve higher mixing intensities, a high-pressure batch homogenizer/mixer was designed and fabricated. In this device, the solute feed solution and aqueous phase streams are pumped separately under high pressure through small orifices, to create two, high-velocity liquid jets that collide head-on in a small mixing chamber filled with the aqueous phase (Figure 4). The intense collision creates a fine-scale, organic-in-water dispersion that is swiftly diluted as the mixture rapidly flows from the mixing chamber into the adjoining, bulk aqueous phase in which the mixing chamber is immersed.23 The mixer was designed to achieve very high mixing energy densities. With a pressure drop of 20.7 MPa, the apparatus can deliver flow rates from 5 to 20 g/s with fluid velocities from 80 to 200 m/s, depending upon the orifice diameter. At these flow rates, the local volumetric rate of dissipation of kinetic energy in the fluid is at least an order of magnitude greater than that produced in the vicinity of the impeller in the batch reactor. (23) Brick, M. C.; Lobo, L. A.; Messner, R. R.; Palmer, H. J.; Whitesides, T. H.; Pike, T. L. U.S. Patent App. Ser. No. 10/119,249, April 9, 2002.

Langmuir, Vol. 19, No. 16, 2003 6371 Analytical Methods. The solubility of the solutes in each organic solvent was determined by allowing an excess of the crystalline phase to equilibrate with the solvent, or solventwater mixture, with agitation for at least 24 h in a thermostated water bath. Next, the supernatant solution was rapidly separated by filtration using a disposable 0.2-µm filter and analyzed for solute by HPLC. The size of the particles formed in the precipitation experiments was measured using dynamic light scattering (Leeds & Northrup MICROTRAC UPA150 particle analyzer). The standard deviation of the modal particle size was about 2.5%, as determined from the mean of 10 replicate measurements on a single sample. Scanning electron microscopy (SEM) was used to examine the particle morphology. SEM samples were prepared by concentrating the quenched samples by centrifugation and adding a dilute, aqueous solution of photographic gelatin in water to prevent particle aggregation during subsequent manipulation. A drop of this preparation was placed on a clean, carbon grid, air-dried at ambient temperature, and vacuum-coated with AuPd. Transmission electron microscopy (TEM) and electron diffraction were used to examine the individual particles for evidence of crystallization. Samples for examination by TEM and electron diffraction were prepared in one of two ways. One method involved putting a thin film of the dispersion onto a carbon-coated, Formvar-substrate copper grid at 25 °C followed by drying in air. Alternatively, a thin film of the dispersion sample was placed on a holey carbon film and dipped into liquid ethane in a controlled environmental vitrification system (CEVS). The samples were examined at 77 K, using a Philips model CM20 transmission electron microscope equipped with a liquid nitrogen cooled stage. The two methods of preparation gave similar results. The same samples were used for electron diffraction studies. Bulk X-ray powder diffraction was used to determine the degree of crystallinity and crystal form of a bulk sample of solute dispersion particles. Samples were prepared for powder X-ray diffraction by centrifuging the dye dispersions and decanting the supernatant solution. The damp solids were packed in an aluminum sample holder or dried on a quartz disk. The samples were examined by X-ray diffraction using a Rigaku RU-300 diffractometer with copper rotating anode, operating at 50 keV and 180 mA.

Results Solubility Experiments. The equilibrium solubility of the crystalline form of D-1 in various NMP-water mixtures at 30 °C is shown in Figure 5. Qualitatively similar results were obtained with all the other solutes and solvents used in the study. In all cases, the solubility decreases dramatically as the water content increases. The solubility of the solutes in the various organic solvent/ water mixtures is correlated quite well with an expression of the form

log10 w1 ) c + dw2 + ew22

(7)

where w1 is the equilibrium solubility of the solute (weight fraction), w2 is the weight fraction of the organic solvent, and c, d, and e are empirical constants. The correlation parameters for each crystalline solute/solvent/water combination are summarized in Table 3. With one exception, the solubility measurements are focused on conditions in which the concentration of organic solvent is less than 0.5 weight fraction, because these are the conditions that were obtained in all of the batch reactor experiments. The solubility of coupler C-1 is immeasurably low at organic solvent concentrations below 0.5 weight fraction. Therefore, the solubility of C-1 in this region was estimated by extrapolating the solubility data measured at organic solvent weight fractions greater than 0.5. Equation 5 was used to estimate the solubility of the amorphous form of each solute, based upon the data in Tables 1 and 3.

6372


Brick et al.

Figure 5. Solubility of crystalline D-1 dye in N-methylpyrrolidinone (NMP)-water mixtures at 30 °C. The data are indicated by the solid symbols. The smooth line is the fitted equation as described in the text. The parameters for the fit are included in Table 3. Table 3. Best-Fit Parameters for Solubility Dataa solute

solvent

c

d

e

D-1 D-1 D-1 D-1 D-1 D-1 D-2 C-1 B-1

NMP DMA DMSO DMF ACN acetone NMP NMP MeOH

-6.55 -6.70 -7.21 -6.72 -6.62 -7.44 -7.69 -12.04 -3.77

8.08 7.98 1.43 6.70 10.83 14.98 9.78 13.70 3.29

-2.15 -1.69 5.04 -0.79 -4.88 -9.32 -0.04 -0.03

a

All regressions yielded a correlation coefficient squared of at least 0.993. The correlation for D-1 and D-2 is valid for 0.5 wt fraction.

Particle Size and Morphology. The effect of process conditions on particle size and morphology was studied most extensively using solute D-1. In particular, precipitation experiments were done with organic feed streams of D-1 dissolved in six different solvents: methanol, ethanol, NMP, DMF, methyl sulfoxide, and acetonitrile. The factors having the largest effect on particle size include the composition of the aqueous phase, specifically the concentration of organic solvent, total dye concentration, and the organic solvent type. The factors having little or no effect on particle size include feed rate, the geometry of the reactor (e.g., feed location and impeller design), solute feed concentration, and the aqueous phase stabilizer level. In all cases, examination by SEM revealed a precipitate comprised of spherical and smooth particles. Typical results are shown in Figure 6. This particle morphology contrasts sharply with the irregularly shaped, roughsurfaced particles produced by milling the crystalline material. The degree of crystallinity of individually precipitated D-1 particles was examined by TEM and electron diffraction. Particles were precipitated from three different solvents (ethanol, methanol, and N-methylpyrrolidone). None of the preparations showed crystalline diffraction patterns using TEM and electron diffraction, even after 1 week of aging. In another technique, the

Figure 6. Scanning electron micrographs of D-1 particles precipitated from (a) N-methylpyrrolidone (NMP) and (b) dimethylacetamide (DMA) for comparison with (c) milled crystalline dye. The precipitated materials consist of smooth spherical particles and lack any indication of ordering by electron diffraction. The milled material consists of angular particles and shows a sharp X-ray powder pattern.

amorphous nature of D-1 particles precipitated from several organic solvent types was confirmed by examination of bulk dispersion samples using X-ray diffraction, immediately after precipitation. Crystallization of the bulk samples did occur over the course of several days (Figure 7). Similar data demonstrated the precipitation of amorphous particles for all of the organic compounds investigated in this study, with one exception. When the most soluble material (B-1) was precipitated using an aqueous phase containing between 10 and 25 wt % NMP, a crystalline precipitate formed. This result is completely consistent with the predictions of eq 5, because for the conditions of these experiments, the solute concentration exceeds the predicted solubility of only the crystalline phase; the solution is not saturated with respect to the amorphous material. Particle-Formation Rates. From measurements of the average particle size D and the cumulative amount of solute added to the reactor mtot(t), the number of particles present in solution, N(t), can be calculated using eq 8

N(t) )

[ ] mtot(t)

FPVP(t)

(8)


Langmuir, Vol. 19, No. 16, 2003 6373

Figure 7. X-ray diffraction patterns of D-1 particles precipitated from N-methylpyrrolidone, for time intervals of 15 min to 12 days after precipitation. A small amount of crystalline material appears after 8 days. Other dispersions of D-1 precipitated from dimethylacetamide, methyl sulfoxide, and acetonitrile also gave similar diffraction patterns at similar time intervals. A pattern of crystalline dye is included for comparison.

Figure 8. Particle number vs time for three D-1 feed solutions in NMP, with 0% NMP in the aqueous solution initially: 2 wt % solute feed, b; 4 wt % solute feed, 4; 8 wt % solute feed, 9. Feed rate is 0.5 total g/s.

where FP is the mass density of the particle and VP(t) ) πD3/6 is the particle volume at time t. In the above equation, it is assumed that all of the added solute is accounted for by the particles because of the extremely low solubility of the solute in the solvent/water phase. Typical results of particle number versus time are presented in Figure 8. These data are for the precipitation of the organic solute D-1 dissolved in NMP on addition to water. Qualitatively similar results were obtained for all the solutes investigated and for a wide variety of process conditions. At any instant in time, the local slope of the

curve is the net particle-formation rate. The highest formation rate occurs at short times, when the number of particles increases approximately linearly with time. The initial particle-formation rate, dN/dt, was taken to be the slope of this line. As can be seen in Figure 8, the particleformation rate decreases in the latter stages of the batch precipitation process. There are at least two reasons for this decrease. As time proceeds, the amount of organic solvent in the precipitation reactor increases and, as we will demonstrate, the particle-formation rate decreases as solubility in the bulk solution increases. Second, at sufficiently high bulk solvent concentrations, growth of the particles by ripening becomes important. Ripening is the result of transport of material from small particles to large ones, driven by surface tension, in accordance with the Kelvin equation.24 This process leads to a net reduction in particle number as small particles disappear at the expense of the growth of large particles. Both of these points will be discussed more fully below. The data presented in Figure 8 indicate that the rate of formation of particles is a function of the concentration of the solute in the organic feed stream; the higher the solute concentration in the feed, the higher the particleformation rate. As stated earlier, the number of particles versus time is computed from direct measurements of the mean particle size. Figure 9 presents the mean particle size (effective diameter) versus time for feed streams containing 2, 4, and 8 wt % of the solute D-1 dissolved in NMP and fed to two different aqueous solutions: one containing 0% NMP, initially, and one containing 17 wt % NMP. In particular, the data set for 0% NMP was used to compute the data presented in Figure 8. The size of the particles at any instant is nearly independent of the feed composition, as long as the amount of organic solvent in (24) Adamson, A. W. Physical Chemistry of Surfaces, 4th ed.; John Wiley: New York, 1982; p 332.

6374


Figure 9. Particle size vs time for three D-1 feed solutions in NMP: lower plot is with 0% NMP in the bulk aqueous solution, initially; upper plot is with 17% NMP in the aqueous solution, initially; 2 wt % solute feed, b; 4 wt % solute feed, 4; 8 wt % solute feed, 9. Feed rate is 0.5 total g/s.

Figure 10. Particle number vs the cumulative amount of solute added during the batch precipitation experiment for three D-1 feed solutions in NMP, with three different levels of NMP in the bulk aqueous solution initially: 2 wt % solute feed, b; 4 wt % solute feed, 4; 8 wt % solute feed, 9. Feed rate is 0.5 total g/s.

the aqueous phase is the same. This outcome was obtained for a variety of process conditions and for all of the organic solutes investigated in this study. Because the mean particle size is independent of the solute concentration in the organic feed stream at a fixed feed rate, i.e., VP(t) is independent of mtot(t), it follows from eq 8 that the three curves presented in Figure 8 should collapse into one curve if the number of particles is plotted versus the cumulative amount of solute added to the precipitator (mtot). This result is presented in Figure 10, not only for the experiments presented in Figure 8 (i.e., 0% NMP) but also for initial NMP solvent levels of 8 and 17 wt % in the aqueous phase. This result, that the number

Brick et al.

Figure 11. Particle number vs the cumulative amount of solute added during the batch precipitation experiment for two D-2 feed solutions in NMP, with 0% NMP in the bulk aqueous solution initially: 2 wt % solute feed, b; 8 wt % solute feed, 9. Feed rate is 0.5 total g/s.

of particles formed versus the cumulative amount of solute added is independent of the feed composition when the feed-flow rate and aqueous phase are held constant, was obtained with the other solutes as well. For example, Figure 11 presents this outcome for the solute D-2. Figures 9 and 10 also illustrate the important effect that the presence of organic solvent in the aqueous phase has on the precipitation process. As the concentration of organic solvent in the precipitating aqueous phase increases, so does the particle size of the precipitate. The observed decrease in particle-formation rate with increasing NMP concentration in the aqueous phase correlates with the associated increase in the equilibrium solubility of the amorphous solute, which varies by a factor of about 60 (from 1.4 × 10-5 to 8.6 × 10-4 weight fraction) as the concentration of NMP in the aqueous phase is increased from 0 to 17 wt %. Similar results were obtained for D-1 in other solvents. Notice also in both Figures 9 and 10 that the results are independent of the solute concentration in the feed, as discussed above, regardless of the amount of NMP present in the aqueous phase at the start of the experiment. The initial particle-formation rate, dN/dt, does not correlate well with the equilibrium solubility of the solute in the precipitating phase, as demonstrated in Figure 12. A better correlation is obtained with a quantity we call the local supersaturation ratio in the vicinity of each drop; defined as

Slocal ) x1/x1*

(9)

where x1 is the concentration of the solute in the organic feed stream and x1* is the equilibrium solubility of the organic solute in the aqueous phase at any instant. Because the solute precipitates as an amorphous solid for all but a handful of experiments, eq 5 is used to compute x1*. Since we have shown above that the particle size is nearly independent of the feed rate for a given solute concentration and precipitant composition, the critical variable is not time but the amount f of solute feed solution added to the reactor. Thus, in Figure 13, we show the


Figure 12. Initial particle-formation rate vs the equilibrium solubility of the amorphous solid phase of the solutes D-1, D-2, and B-1 for precipitation experiments done with feed solutions made with a variety of organic solvents. With one exception, the feed-flow rate is 0.5 total g/s. The open triangles, 4, are for D-1 in NMP at 1.0 g/s. The organic feed streams are as follows: D-1 in ACN, 1; D-1 in NMP, 2; D-1 in DMSO, b; D-1 in DMA, 9; D-2 in NMP, [; B-1 in MeOH, ].

Figure 13. Initial particle-formation rate vs local supersaturation for experiments done with feed solutions made with a variety of organic solvents. With one exception, the feed-flow rate is 0.5 total g/s. The open triangles, 4, are for D-1 in NMP at 1.0 g/s. The organic feed streams are as follows: D-1 in ACN, 1; D-1 in NMP, 2; D-1 in DMSO, b; D-1 in DMA, 9; D-2 in NMP, [; B-1 in MeOH, ].

dependence of the particle-formation rate per gram of solute feed, dN/df, as a function of the local supersaturation as defined by eq 9. Figure 13 presents the good correlation obtained between initial particle-formation rate, represented as dN/df, and local supersaturation rate over all solvent types. For a single solute, the correlation is reasonably strong and can be improved further if we assume a weak dependence on the feed solute concentration. Figure 14 shows the correlation when this dependence (x0.6) is taken

Langmuir, Vol. 19, No. 16, 2003 6375

Figure 14. The same data as in Figure 13, with a weak dependence on the feed solute concentration (xfeed0.6) incorporated into the variable plotted on the x-axis. The collapse of the data to a single master curve is improved. The symbols have the same meaning as those in Figure 13.

into account. Data for other solutes do not appear to fall on the same line. The rate of particle formation presumably depends on details of the chemical potential of the solute in solution that vary appreciably from compound to compound. In all experiments, the particle-formation rate decreases with time as subsequent additions of solute to the reactor contribute to particle growth as well as particle formation (see Figure 8). For small values of the supersaturation, i.e., Slocal < 102, corresponding to very high solvent concentrations in the aqueous phase, the effect of particle growth and ripening on the number of particles versus time was so pronounced that, in some cases, a decrease in the total number of particles was observed during the latter stages of the experiment. To determine the extent to which particle growth and ripening were significant factors in the precipitation experiments, experiments were carried out in which the addition of feed solution was halted after a certain time and the particle size in the reactor was monitored by removing and quenching aliquots by dilution with water. Typical results for D-1 in NMP (at initial concentrations of 2, 11, and 26 wt % organic solvent in water) are shown in Figure 15. If the ripening rate is low, then the particle size should not change significantly. This was true for solvent concentrations in the aqueous phase below about 10 wt %. However, for larger solvent concentrations, it is clear that particle growth by ripening is significant within the time frame of a precipitation experiment. The slope of each line in Figure 15 is the particle growth rate. Figure 16 presents the results of several such experiments as particle growth rate as a result of ripening versus the equilibrium solubility of the amorphous state at the experimental conditions. In our experiments, the testing variability in the measurement of a 0.2 µm diameter particle is 5% (0.01 µm). Over an average batch time of 30 s, this corresponds to a change in particle diameter of 3 × 10-4 µm/s. Thus, from Figure 16, we can conclude that the effect of ripening on the observed growth rate of particles is negligible if the solubility of the amorphous state in the aqueous phase is less than ∼10-4 mole fraction solute. The apparent

6376


Brick et al. Table 4. Upper Useful Solute Feed Concentration and log (P) of Organic Solutes

Figure 15. The evolution of particle size over time for solute D-1 in aqueous suspensions of differing NMP composition: 26 wt % NMP, b; 11 wt % NMP, 0; 2 wt % NMP, 2. The solubility of amorphous D-1 is 1.2 × 10-3, 9.0 × 10 -5, and 1.7 × 10-5 (weight fractions), respectively, in these solutions.

Figure 16. Rate of growth of particle size for solute D-1 in NMP/water mixtures as a function of the solubility of the amorphous solute. The dotted line is a linear fit to the data, constrained to go through the origin. The slope is 54 µm s-1 (mole fraction)-1.

particle-formation rate also decreases markedly at high solute feed concentrations. In this regime, microscopic examination of the resulting dispersions revealed that substantial numbers of very large particles were formed, apparently as a result of flocculation. At still higher feed concentrations, a substantial amount of coagulum also formed. The feed solute concentration corresponding to the onset of this failure mechanism varied, depending upon the organic solvent, and correlates with the hydrophobicity of the solvent, as shown in Table 4. We believe that in this regime the rate of stabilization of the colloidal particles is slower than collision and coalescence. High-Energy Mixing. Results from initial screening effects of process variables showed that rotary impeller

organic solvent

wt % D-1 in feed for onset of flocculation

solvent log (P)

tetrahydrofuran (THF) acetonitrile (ACN) N-methylpyrrolidinone (NMP) dimethylacetamide (DMA) methyl sulfoxide (DMSO)

∼1 ∼1 ∼10 ∼10 ∼15

0.33 -0.39 -0.73 -0.77 -1.38

types and mixing speeds from 50 to 400 revolutions/min had no significant effect on dispersion particle size. However, very vigorous mixing conditions, using the highpressure impingement device described in the Experimental Section, resulted in a decrease in particle size. The energy of mixing in the high energy mixing device can be varied by changing the pressure drop and the diameter of the orifices through which the solutions are forced to make the jets. With conditions that afforded a mass flow rate of approximately 5 g/s and fluid velocity of approximately 160 m/s in each fluid stream with a feed concentration of 4 wt % D-1, the average particle size produced was 0.10 µm. A similar batch process using conventional impeller mixing and the same solute feed concentration gave a larger particle size (0.19-0.21 µm). Discussion Mechanism of Particle Formation. We consider two classes of mechanism. In the first, the organic (feed) phase containing solute is completely and homogeneously mixed with the bulk aqueous solution upon entering the reactor, instantaneously forming a molecular solution of solute in a largely aqueous medium. This scenario presumes that the blending rate and the associated process of molecular diffusion are extremely rapid, as compared to the rate of nucleation. Because the solutes in this work are very insoluble in water, the resulting solution is in a highly supersaturated state and, thus, the solute separates into small particles by a nucleation and growth mechanism occurring throughout the bulk solution. In the second class of mechanism, the feed solution is not homogeneously mixed before the phase-separation process begins. Instead, the feed is rapidly dispersed as droplets or streamers. These droplets exchange organic solvent and water with the bulk phase, largely by diffusion, and phase separation occurs within the droplet as supersaturation on a local scale is achieved. This mechanism is illustrated schematically in Figure 17. The process of phase separation within the droplet could itself proceed by nucleation and growth or by a process of spinodal decomposition (spontaneous phase separation). If it were to proceed by a nucleation and growth process, we would expect nucleation to be dominated by homogeneous nucleation by a simple counting argument: with any reasonable degree of droplet dispersion, there are many more droplets than available heteronuclei. Spinodal decomposition, on the other hand, is characterized by the rapid growth of concentration fluctuations of solute leading eventually to the separation of a compositionally stable phase rich in solute. The particle size in this process will be determined by a competition between solvent-nonsolvent counterdiffusion and the growth rate of the amplitude of the fluctuations. First consider the hypothesis that the mixing is instantaneous, thereby creating a homogeneous, single phase from which solute particles are formed by nucleation and growth. There are several prominent features of our results that are difficult to rationalize within the context of this model. Because we have taken only moderate precautions to exclude dust particles and other adventi-


Langmuir, Vol. 19, No. 16, 2003 6377

Figure 17. Schematic description of preferred mechanism for particle formation. Droplets are formed by dispersion of the feed solution into the bulk. This process is followed by rapid counterdiffusion of solvent and water, leading to phase separation by spinodal decomposition. Within the droplet, particles begin to form as large-scale fluctuations in the concentration of solute, the amplitude of which is indicated by the intensity of gray shading. The size of the condensing region, because it includes more solvent, is larger than the particle that is finally formed, shown as the black dots around the outside. The size of the condensing region decreases, and the concentration of solute increases as the amount of water increases, which happens as the edge of the original droplet is approached. After most of the solvent is gone, the particles are dispersed into the bulk solution as a random spray, where they are stabilized by surfactant.

Figure 18. Schematic phase diagram (lower plot) and the associated free energy diagram (upper plot) for a liquid-liquid phase separation resulting from solvent shifting. As discussed in the text, the separation process is described as a function of the solvent composition, where Co indicates pure organic solvent and C1, C2, and C3 are differing pseudosolvent compositions containing increasing quantities of water. On the phase diagram, the one- and two-phase regions are indicated, together with the binodal and spinodal lines. The vertical dotted lines show the connection with the corresponding points on the free energy diagram. The heavy arrow shows a possible trajectory resulting from diffusional mixing of a dispersed solution feed droplet with water resulting in spinodal decomposition of the droplet into a solute-rich amorphous particle.

tious nuclei from our experiments, we should expect that heterogeneous nucleation would dominate the particleformation process. The good reproducibility of our results is surprising in the light of this expectation. Furthermore, we find that the mean particle size is nearly independent of a variety of experimental parameters, including solute feed concentration and feed rate. If the solute were homogeneously dispersed before precipitation, both of these variables would influence the degree of supersaturation and, thus, the rate of nucleation and also that of the growth process. Both of these processes would affect the particle size in ways that would be unlikely to compensate closely. This would be particularly true later in a batch reaction, when the presence of large numbers of previously formed particles should strongly suppress nucleation, and substantial particle growth should be observed. Another prominent feature of our results is the substantial reduction in particle size in precipitations carried out using the high-energy impingement-mixing device. If the mixing process in the batch reactor had been virtually instantaneous with the rotary impeller, the very high mixing intensities produced in the impingementmixing device should not have had any further effect on particle size. Further, the universal formation of amorphous particles, observed not only in the results reported here but also widely in the literature in similar situations, is not easy to explain because, in all cases, the crystalline solid is the thermodynamically favored state. In summary, our experimental observations appear to be inconsistent with a particle-formation model that is based upon the

instantaneous formation of a homogeneous phase followed by nucleation and growth. In contrast, particle-formation mechanisms that involve phase separation from dispersed feed solution droplets, before complete mixing can occur, can provide explanations for all of our results. The situation is simplified substantially by the observation that the phase that separates is the amorphous solid, which we view as thermodynamically indistinguishable from the supercooled liquid phase of the solute. A schematic phase diagram and associated free energy diagram of liquid-liquid phase separation during solvent shifting is shown in Figure 18. In this diagram, we consider the system as consisting of two components: (1) the solute and (2) a binary pseudosolvent comprising a specified mixture of solvent and nonsolvent (i.e., water). Each curve on the upper diagram corresponds to a single composition of the pseudosolvent, ranging from pure organic solvent (Co), in which the solute is relatively soluble, to composition C3, rich in nonsolvent, in which the solute is very insoluble. In this diagram, the composition of the binary solvent is the thermodynamic variable, taking the place usually occupied by the temperature in a diagram of this sort. The lower plot of the figure is a phase diagram that shows the stability regions that correspond to the change in solvent composition (the ordinate in this diagram) from Co to C3 and solute concentration from 0 to 1 (abscissa). By analogy to conventional phase diagrams, with temperature on the ordinate, the binodal curve is the locus of the compositions into which a given mixture separates

6378


at thermodynamic equilibrium and, thus, divides the phase diagram into the one-phase and two-phase regions. The spinodal curve is defined as the locus of inflection points on each curve of the free energy (upper) diagram; that is, the points where (∂2∆Gmix/∂X2)T,C ) 0. Within the two-phase region, the spinodal curve separates the unstable region, where concentration fluctuations are expected to grow, from the metastable region, where phase separation is thermodynamically favored but where sufficiently small concentration fluctuations do not grow spontaneously. In the regime between the binodal and spinodal curves, nucleation-and-growth mechanisms are expected to apply to the phase-separation process.16-18,25 The phase-separation process in our solvent-shifting process can be depicted as a trajectory in the phase diagram represented by the bold arrows. Note that the arrows in the upper and lower parts of the diagram refer to the same trajectory. We begin with a feed solution undersaturated with solute, represented by point a at a pseudosolvent composition Co in the one-phase region in Figure 18. If we imagine a droplet of this solution suspended in water as a result of rapid dispersion by the mixer, counterdiffusion of solvent and nonsolvent at the interface of the droplet will occur. The solute near the interface will find itself in a local medium of progressively poorer solvent quality (i.e., the compositional trajectory abc in the lower graph). At some point during the mixing process, the local composition will cross through the binodal line into the metastable region (point b). If the compositional environment were to be “frozen” at point b, phase separation might eventually take place by (homogeneous) nucleation and growth. However, because the solutes in our experiments are very insoluble, the droplets are small, the fluid turbulence is intense, and the diffusive transport process will continue to occur at a rapid rate (diffusive flux being inversely proportional to the droplet radius), thereby moving the local process conditions further along the abc trajectory and into the spinodal region (to point c) before nucleation has a chance to occur. Once this point is reached, the solution will become unstable, concentration fluctuations of the solute will grow exponentially, and phase separation will occur spontaneously.26 Finally, the particles are further dispersed into the bulk, where they are stabilized by adsorption of surfactant and polymeric stabilizer The growth process will occur on a characteristic length scale, the critical fluctuation length, CFL. The CFL in this dynamic process is more complex than in the spinodal phase-separation processes studied in the literature, since the solvent quality continues to change during the growth process, and the most rapidly growing fluctuation length decreases with increasing quench depth (corresponding to poorer solvent quality). Ultimately, we expect the process at completion to occur on a length scale that is determined by a combination of the rates of diffusion of the solvent/nonsolvent pair (which results in progressively poorer local solvent quality) and the motion of the solute (i.e., how rapidly the growth of concentration fluctuations can proceed). In this picture, the solute contained within one CFL will form a single particle. We can estimate the CFL operationally by determining the average particle size and calculating the volume of the feed solution from which it must have arisen. The volume of feed solution that gives rise to a given particle is equal to the particle volume divided by the solute feed concentration. The CFL (25) Goldburg, W. I. In Light Scattering Near Phase Transitions; Cummins, H. Z., Levanyuk, A. P., Eds.; Modern Problems in Condensed Matter Sciences, North-Holland: Amsterdam, 1983; Vol. 5, Chapter 9. (26) Cahn, J. W. J. Chem. Phys. 1965, 42, 93.

Brick et al.

is taken to be the cube root of this volume, so that CFL ≈ (dp/Cfeed1/3). For example, for a 5 wt % feed resulting in a 0.25 µm particle (typical of our observations), the CFL is estimated to be less than a micrometer. Because the spinodal decomposition mechanism describes a liquid-liquid phase-separation process with no necessity to nucleate crystalline material, the formation of particles of amorphous solute is readily understood. As long as the mixing process disperses the feed solution into the aqueous phase as droplets that are larger than the CFL, the particle size is determined by the competition of the diffusive processes described above, and the resultant particle size will be independent of the mixing rate, as observed. Conversely, if the intensity of mixing is sufficient to produce elementary feed droplets that are smaller than the CFL (such as in the impingement mixer), the particle size will not be limited by the diffusional process but, instead, by the solute available within the small dispersed droplet. Thus, a particle size reduction by this mechanism would be expected only with very energetic mixing. Finally, the spinodal decomposition mechanism is also consistent with the observed variations of the particle size with the composition of the bulk solution. We observe that the particle size increases as the local supersaturation is decreased. This effect can be rationalized as a reduction in the depth of quenching into the spinodal region of the phase diagram when solvent is added to the bulk phase. As the amount of solvent increases, the degree of supersaturation (that is, the quench depth) achieved in the zone of counterdiffusion in the dispersed feed droplets is reduced. This reduction should result in an increase in the CFL and, thus, the formation of larger particles. If the CFL were independent of the solute feed concentration, the particle size would be expected to increase with (Cfeed)1/3, and the number of particles formed per volume of feed to increase linearly with Cfeed. However, increasing the solute feed concentration would also increase the local supersaturation, and this effect would be expected to decrease the CFL somewhat, so we might expect a somewhat less-than-linear dependence on the feed concentration. We observe that the particle size depends only weakly on the feed concentration (Figure 9). From the collapse of the particle-formation rate data in Figures 13 and 14, the estimated concentration dependence is xfeed0.6, a result that is consistent with our expectations. Particle Size and Mixing. We now consider the effect of the mixing intensity in more detail. The mixing process can be characterized by the specific energy dissipation rate, , which is the rate per unit mass at which mechanical energy is converted to thermal energy through viscous dissipation.27,28 The specific energy dissipation rate can be used to estimate a characteristic length scale for mixing, η, called the Kolmogorov turbulent eddy size. In the present context, η can be viewed as a measure of the characteristic size of the feed solution droplet as it is dispersed into the bulk solution by fluid turbulence. For a specific energy dissipation rate and kinematic viscosity ν, the Kolmogorov turbulent eddy size is given by29

η ) (ν3/)1/4

(10)

(27) Whitaker, S. Introduction to Fluid Mechanics; Krieger Publishing Company: FL, 1992; Chapter 7. (28) Bird, R. B.; Stewart, W. E.; Lightfoot, E. N. Transport Phenomena; John Wiley: New York, 1960; Chapter 3. (29) Tatterson, G. B. Fluid Mixing and Gas Dispersion in Agitated Tanks; McGraw-Hill: New York, 1991; p 125.


In the batch reactor used in this study, the mixing energy originates from the turbine impeller. This impeller is capable of producing a specific energy dissipation rate in the range of ≈0.2-1.5 W/kg,30 corresponding to a Kolmogorov mixing length scale η of approximately 3050 µm. Notice that this mixing length is much greater than our estimate of the CFL (≈1 µm). Therefore, it is reasonable to expect that many particles will form within a single droplet of feed solution, which accounts for the fact that the particle size is barely dependent on the mixing rate in this mixing regime. By use of the impinging jet mixing device, much higher mixing energies are obtained. With fluid velocities of 160 m/s in each stream and a mixing chamber volume of 5 × 10-11 m3, the energy density ≈ 3 × 109 W/kg. The Kolmogorov mixing scale for this energy density is η ≈ 0.2 µm. This length is substantially smaller than the CFL estimated on the basis of the low energy experiments. Thus with this device we expect that the particle size would be smaller than that obtained using the batch reactor. This is what is observed: a feed solution giving a particle size of about 0.2 µm in the batch reactor yielded a particle size of 0.1 µm in the impingement mixer. The time scale for particle formation in the dispersed droplet can be estimated from the CFL using a diffusion constant of about 10-5 cm2/s, characteristic of the motion of small molecules in aqueous media. Using a CFL ≈ 1 µm, the time scale for diffusional mixing is less than 1 ms, suggesting that the particles are formed very rapidly at the periphery of the droplet/bulk interface and the droplet itself persists for a substantial period of time, possibly shedding particles of precipitated solute from its edges. Practical Limitations to Solvent Shifting Flocculation. Colloidal instability was observed under several experimental conditions. At local supersaturation values above 105, the ability to produce fine colloidal dispersions was compromised by particle agglomeration, which was detected by microscopic examination of the precipitate. To achieve these high levels of local supersaturation, it was necessary to use both high solute feed and low bulk solvent concentrations. At these levels, it is possible that the local rate of formation of particles is so rapid that the local supply of stabilizer is depleted, resulting in irreversible flocculation before the particles are fully dispersed into the aqueous phase. It was also observed, however, that the maximum solute feed concentration varied systematically with the type of solvent in a way that correlates roughly with the hydrophobicity of the solvent as measured by the octanol/water partition coefficient, log Pcalc (Table 4). The less hydrophilic the solvent, the lower the maximum solute feed concentration that is possible without substantial flocculation and coagulum formation. Further, the morphology of the particles formed from some of these solvents was observed to change from discrete, sub-micrometer spheres to particles encapsulated within larger spheres up to 20 µm in diameter. A possible explanation of this effect is that the more hydrophobic solvents are reluctant to partition rapidly into the aqueous phase, leaving a particle that is, at the same time, more deformable and less stabilized by the surfactant/polymer mixture. Particle Growth. Another limitation to the solventshifting process is particle growth at low supersaturations, (30) Calculated using a power number of 5, a diameter of 0.04 m, speeds of 200-400 revolutions/min, and a kinematic viscosity v ≈ 10-6 m2/s. The power number is taken from Tatterson, G. B. Scale-up and Design of Mixing Processes; McGraw-Hill, Inc.: New York, 1994; Chapter 2.

Langmuir, Vol. 19, No. 16, 2003 6379

corresponding invariably to high organic solvent and high bulk solubility. We attribute the particle growth in this regime to ripening by molecular transport (Ostwald ripening). Particle growth rates are correlated with the bulk equilibrium solute solubility (Figure 16). It is worth reemphasizing that ripening rates are very slow under conditions corresponding to most of our precipitation data. Conclusions We show that solvent shifting can be used to prepare organic particles of colloidal dimensions at relatively high particle concentrations. The particle size can be controlled over a limited range by manipulating the local supersaturation, specifically by incorporating organic solvent into the bulk phase. We show that this technique is applicable to a variety of organic materials and several organic water-miscible solvents. Conditions to produce small particles are greatly enhanced if the organic solute is very insoluble in the aqueous phase so that high supersaturation and high rates of particle formation can be achieved. We further show that the process of particle formation can be easily understood in terms of a mechanism involving dispersion of the solute feed solution into the nonsolvent phase as discrete particles, followed by counterdiffusion of solvent and nonsolvent. The rapid change in solubility leads to a phase separation of the solute by a process analogous to spinodal decomposition. All of the observed experimental phenomena are economically explained by this mechanism. List of Symbols a An b c Cn Cfeed C ˆP d D e f G G ˆ ∆Gmix H ˆ ∆H ˆM J k mtot n N Rg S S ˆ ∆S ˆM T w x VP Υ

activity nucleation constant, nuclei mL-1 s-1 heterogeneous nucleation rate factor empirical constant for solubility in eq 7 pure or pseudosolvent feed composition, weight fraction feed concentration, weight fraction solute molar heat capacity at constant pressure empirical constant for solubility in eq 7 average particle size, µm or cm empirical constant for solubility in eq 7 amount of feed solution added to reactor, g Gibbs free energy, kJ Gibbs free energy per mole, kJ mol-1 Gibbs free energy of mixing, kJ enthalpy per mole, kJ mol-1 molar enthalpy of melting, kJ mol-1 nucleation rate, nuclei mL-1 s-1 Boltzmann constant, 1.3805 × 10-23 J K-1 mol-1 total mass of solute added to reactor, g number of moles number of particles universal gas constant, 8.314 J mol-1 K-1 supersaturation ratio molar entropy, kJ mol-1 K-1 molar entropy of melting, kJ mol-1 K-1 absolute temperature, K weight fraction mole fraction volume of a particle, (cm3) molecular volume, mL molecule-1

Greek Letters γ

activity coefficient

6380 η µ ν FP σ υ

Langmuir, Vol. 19, No. 16, 2003 specific energy dissipation rate, m2 s-3 Kolmogorov length scale, m chemical potential, kJ mol-1 kinematic viscosity, m2 s-1 density of a particle, g (cm3)-1 interfacial tension, J m-2 velocity, m s-1

Superscripts/Subscripts (A) (C)

amorphous state crystalline phase

Brick et al. M 1 2 * ∧

melting, melting point organic solute organic solvent saturated solution thermodynamic properties on a per mole basis

Acknowledgment. The authors thank Eastman Kodak Company for the financial support of this study. LA034173O

Formation of Colloidal Dispersions of Organic Materials in Aqueous

Recommend Documents