Demonstration of Mechanisms for Coprecipitation and Encapsulation

Dec 17, 2010 - Supercritical antisolvent process is a proven method for micronization and encapsulation of solute(s) dissolved in a solvent. When solu...
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Ind. Eng. Chem. Res. 2011, 50, 1079–1088

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Demonstration of Mechanisms for Coprecipitation and Encapsulation by Supercritical Antisolvent Process Rajarshi Guha, Madhu Vinjamur,* and Mamata Mukhopadhyay Department of Chemical Engineering, IIT Bombay, Powai, Mumbai 400 076, India

Supercritical antisolvent process is a proven method for micronization and encapsulation of solute(s) dissolved in a solvent. When solution contains one solute, it is micronized to produce small particles; when solution contains two solutes, they either coprecipitate, or one of them encapsulates the other. Experiments with several systems for micronization and encapsulation have been described in the literature. In this work, a model has been developed for the process in which supercritical carbon dioxide flows countercurrently or cocurrently to an atomized solution. The model includes mass transport of the solute(s) and carbon dioxide, supersaturation, nucleation, and growth of particles of solute(s). Criteria for coprecipitation and encapsulation were identified, and on the basis of model predictions a new mechanism is proposed to explain the criteria. A solute encapsulates another solute if supersaturation of the former becomes high near the end of the process and it grows on the latter. If high supersaturation is attained during the process, they coprecipitate. Introduction Supercritical fluid-assisted precipitation processes are green technologies, which can be used to produce micrometer-sized and encapsulated powder mainly for the pharmaceutical, polymer, and catalyst processing. Micronization here is defined as the process of producing small solute particles from a solution sprayed in flowing/stationary supercritical carbon dioxide due to its antisolvent effect. Encapsulation here is defined as the process of producing small particles when a solution consisting of two solutes and a solvent is sprayed in flowing/stationary supercritical carbon dioxide (SC CO2) in which one solute grows over already precipitated solute particles. As soon as the solution is sprayed through a nozzle and drops are generated, carbon dioxide diffuses into them. Because of the antisolvent effect, the solubility of solute falls rapidly, and the drop becomes supersaturated with the solute. Nuclei of the solute form, and they grow to produce particles. Encapsulation occurs if one solute precipitates over the other and simultaneously grows. One of the most popular precipitation processes is the supercritical antisolvent (SAS) process in which carbon dioxide dissolves in drops of a sprayed solution and due to the antisolvent effect reduces solubility of solute resulting in its precipitation to produce fine particles. The merits of the SAS process are lower operating temperature than that used in spray drying and lower residual solvent content. Also, mean particle size, particle size distribution, and morphology can be controlled by changing process parameters such as pressure and temperature. Several materials have been micronized and encapsulated using SAS process. Encapsulation of suspended hydrophobic and hydrophilic silica nanoparticles with Eudragit polymer dissolved in acetone has been reported.1 When the polymer solution was sprayed in a vessel containing SC CO2, the polymer precipitated out due to antisolvent effect of CO2, and it then grows on suspended silica particles. Martin2 described precipitation of micrometer-sized particles of budesonide and budenoside encapsulated by poly (lactic acid) with a compressed antisolvent method. Their method resulted in high encapsulation efficiency (about 80%). Diego et al.3 proposed that, below mixture critical pressure, particles precipitate by phase separation of a * To whom correspondence should be addressed. Tel.: +91-22-2576 7218. Fax: +91-22-2572 6895. E-mail: [email protected].

liquid-liquid mixture. Above this pressure, no interface exists, and smaller particles that do not agglomerate are produced. They produced small particles from a solution containing poly (Llactic acid)-cholesterol in dichloromethane using a compressed antisolvent method. They observed that with rising cholesterol concentration, fibrous and less agglomerated spherical-shaped particles are produced with an improved SAS process at a temperature of 35 °C, pressure of 120 bar, using a cholesterol to polymer weight ratio of 1:10. Charbit et al.4 studied encapsulation of a herbicide, Diuron, in biodegradable L-poly (lactic acid). They observed that at smaller polymer to solute ratios (2:1) and at 35 °C and 100 bar pressure, long needles of polymer and small Diuron particles coprecipitated. However, when the ratio was raised to 10, smaller encapsulated spherical particles were produced when other conditions were maintained. The size of particles precipitated by supercritical fluid antisolvent processes can be controlled by adjusting parameters such as temperature, pressure, initial solute concentration, polymer molecular weight and its weight fraction, solution flow rate and ratio of flow rates of SC CO2 to that of feed solution, nozzle diameter, nature of solvent, density of SC CO2, and presence of surfactant or stabilizer. Kim et al.5 and Chen et al.6 showed that particle size falls with rising pressure. At higher pressures, the diffusion driving force increases along with the solubility. This increase causes considerable decrease in partial molar volume and cohesive energy density of the solvent, which eventually reduces the solvent strength for the solid solute and causes a higher degree of supersaturation, faster nucleation, and resultant smaller particle size.5 The particle size rises with the solute concentration. When the concentration is low, saturation followed by precipitation occurs late during droplet expansion process. This lag allows nucleation, but not much growth within the precipitation time, and results in generation of smaller particles. When the concentration is high, particles precipitate early during expansion, and growth dominates over nucleation leading to rise in particle size.5 An increase in size of precipitated particles with solute concentration has been observed in several studies.6-8 The particle size falls with rising CO2 flow rate. As CO2 flow rate rises, the initial drop diameter and evaporation time are reduced, and the mean particle size also falls.8,9 The ratio of flow rates of CO2 to feed solution in the range of 40-60 has

10.1021/ie101449a  2011 American Chemical Society Published on Web 12/17/2010

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Figure 1. Schematic of supercritical carbon dioxide pilot plant in which SAS process was used for coprecipitation and encapsulation (1, cylinder; 2, condenser; 3, storage tank; 4, precooler; 5, diaphragm pump; 6, preheater; 7, control valve; 8, precipitation vessel with nozzle; 9, separator; 10, solvent release valve; 11, feed charge; 12, solvent pump; 13, solution control valve).

been observed to give smaller mean particle size and narrower particle size distribution.5 Considerable efforts have been made to model SAS process to predict effects of operating temperature and pressure on properties such as drop diameter, CO2 mole fraction, temperature of solution, and supersaturation of the solute followed by its nucleation in a drop during the process.10-14 This work presents modeling of micronization by SAS process starting from single droplet evaporation to supersaturation, nucleation, and growth. The model predicts mean size of the particles and their size distribution for single-solute systems. The model has been extended to the two-solute system and to propose new mechanisms for encapsulation and coprecipitation. Also, experiments have been carried out with the cholesterol-dichloro methanepoly (L-lactide)-SC CO2 system to study the effect of ratio of solute to polymer on particle morphology, mean particle size, coprecipitation, and encapsulation. Criteria for coprecipitation and encapsulation have been developed and validated by experimental results. Experiments Materials. Crystalline poly (L-lactic acid) (PLA) (molecular weight 99 000) was purchased from Aldrich Chemicals. HPLC grade dichloro methane (DCM) (99.5% purity) was obtained from Merck. Cholesterol (99% purity) was supplied from Loba Chemie (India). Carbon dioxide was supplied in standard cylinders. Equipment and Procedure. Figure 1 shows the schematic diagram of a pilot plant used for the experimental SAS process. Carbon dioxide was liquefied in condenser (2) and stored in a tank (3). Liquid CO2 was further cooled in a precooler (4) to avoid cavitation in the pump (5). Supercritical conditions were attained by heating the compressed CO2 in a preheater (6). CO2 was then made to flow through a precipitation vessel (8) in which a solution, containing cholesterol and/or PLA dissolved in DCM, was pumped and atomized through a nozzle. The mode of flow of solution and carbon dioxide can be cocurrent or counter current. Countercurrent flow was observed to give higher yield and smaller particles. The solvent separated out from carbon dioxide in a separator (9). The solvent-free carbon dioxide was then recycled to the condenser (2). At the end of the experiments, the vessel was flushed with carbon dioxide for some time to remove any traces of solvent vapor. The system was depressurized, and particles formed were collected from the vessel.

Product Analysis. The particles were characterized with QUANTA 200 E-SEM (environmental scanning electron microscope) in a low vacuum mode. The mean particle size and particle size distribution have been analyzed using image analysis software, ImageJ (An image processing program developed at the National Institutes of Health, and downloaded from the Institutes’ Web site). A simple “two-solvent” method has been used to know whether coprecipitation of cholesterol and PLA or encapsulation of cholesterol with PLA has taken place. In this method, a sample of particles was first treated with acetone in which cholesterol is soluble but PLA is not. Cholesterol that is not encapsulated with the polymer will dissolve in acetone. A difference in the weights of acetone and acetone with dissolved cholesterol gives the weight of cholesterol that is not encapsulated. The residual material can be collected and treated with water, which dissolves PLA but not cholesterol. During this dissolution, suspension of particles (of cholesterol) indicates encapsulation, and clear solution indicates coprecipitation. The weight of suspended particles is noted by filtering the solution and drying the filter. Encapsulation efficiency, EE, was calculated as follows: % EE ) encapsulated cholesterol × 100 encapsulated cholesterol + unencapsulated cholesterol Experimental Results and Discussion The system studied was a solution of cholesterol and PLA in DCM. The solution was sprayed in a vessel into which SC CO2 was also passed, either cocurrently or counter-currently. Operating temperature and pressure were 45 °C and 90 bar. SEM images of cholesterol particles used to prepare solutions showed that they were flaked and agglomerated (Figure 2a and b). When a solution containing cholesterol (2.9 wt %) and PLA (0.58 wt %) in a ratio of about 5:1 was sprayed at a rate of 0.6 kg/h and CO2 was passed at 48 kg/h, long needle-shaped particles were formed as shown in Figure 2c and d. When the ratio was reduced to about 0.5:1, cholesterol concentration being 0.24 wt % and that of the polymer 0.5 wt %, encapsulated spherical particles were formed (Figure 2e and f). The average particle size and standard deviation for Figure 2a-f are shown in Table 1. Higher polymer content than cholesterol not only reduced the particle size but also changed the morphology from coprecipitated needles to encapsulated spheres with an encapsulation efficiency of 32% measured by the two-solvent method discussed in the previous section. Many researchers observed the effect of higher polymer content on morphology of particles using the SAS process: Martin et al.2 showed images of poly (lactic acid) encapsulated budesonide particles with a solution containing 0.1 and 0.5 wt % of the latter and 1 wt % of the former in methylene chloride; Taki et al.15 showed that spherical particles of poly (lactic acid) encapsulated a herbicide, diuron, when the concentration of the former was 1 wt % and the latter was 0.1 wt % in DCM. Our experimental findings are similar to the above-described observations. Model Equations To understand the effect of weight ratio of polymer to cholesterol on particle size and size distribution, a model for SAS process was developed for particle formation from a drop of solution. The model includes all the steps involved in droplet evaporation and particle formation as shown in Figure 3. As the droplet emerges out of the nozzle, carbon dioxide diffuses into it, and the solvent evaporates out of it. The droplet swells

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Figure 2. SEM micrographs of particles produced from solutions of cholesterol and solutions of cholesterol and PLA in dichloromethane. Operating temperature and pressure were 45 °C and 90 bar, respectively. (a) Flake shaped feed cholesterol particles, processing at 250×, (b) agglomeration of cholesterol particles in feed, processing at 500×, (c) coprecipitation of PLA and cholesterol from a solution containing 0.58 wt % PLA and 2.9 wt % cholesterol, processing at 1200×, (d) magnified picture of (c) showing fiber or needle shaped particles, processing at 5000×, (e) encapsulation of PLA and cholesterol from a solution containing 0.5 wt % PLA and 0.24 wt % cholesterol, processing at 2500×, and (f) magnified image of (e) showing uniform encapsulated cholesterol particles, processing at 6000×. Table 1. Average Size and Standard Deviation of Pure Cholesterol Particles, Coprecipitated Cholesterol and PLA Particles, and Encapsulated Cholesterol with PLA Particles

system cholesterol 2.9 wt % cholesterol and 0.58 wt % PLA in DCM 0.24 wt % cholesterol and 0.5 wt % PLA in DCM

average particle size (µm) 42 8 1.7

standard deviation (µm) 18 4.7

As the CO2 enters the drop, solute solubility falls due to antisolvent effect of CO2. Next, the solution becomes supersaturated with the solute. In SAS process, a high supersaturation is achieved quickly, and a large number of small nuclei form, which grow to produce particles of micrometer and submicrometer size. In the model, equations are written for dynamics of a single droplet assuming that there is no solvent in the bulk CO2 because the ratio of flow rates of CO2 to solution is high.

0.9

initially because the rate at which CO2 diffuses into it is greater than the rate at which the solvent leaves the drop. Subsequently, however, the drop shrinks because of a higher rate of solvent loss.

Drop Diameter The diameter of the drop, do, emerging from the nozzle depends on the velocity at the exit of the nozzle, and physical properties such as surface tension, viscosity, density, and nozzle

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Figure 3. Schematic of different steps during particles formation from a drop by SAS process.

diameter. It can be found by a correlation proposed by Mugele16 as follows:

( ) ( )

do ) 5dn

dnFLuL µL

-0.35

µLuL σL

The binary diffusion coefficient for liquid, DL, is calculated by the Vigens correlation: DL ) (DLo)1-x1(DGo)x1

-0.2

(1)

FL is liquid density (kg/m3), dn is the nozzle diameter (m), µL is liquid viscosity (Pa · s), σL is interfacial tension between gas-liquid (N/m), and uL is liquid velocity (m/s).

o

DL and DG are infinite dilution liquid diffusivity and infinite dilution gas diffusivity, respectively. These were calculated via the Wilke-Chang equation and its modified form. Drop velocity, V, is calculated by balancing gravity, buoyancy, and drag forces:

(

FL - FG 18µGV dV ) g dt FL FLd2

Mass Transfer Correlations for mass transport coefficient are not available at high pressures for liquid systems. Hence, it is considered that the Hughmark correlation for liquid-liquid spray systems17 is applicable for spraying of a solution in supercritical fluid. In a few publications, Hughmark correlation was used, and results have been verified with experiments.11-13 Hughmark correlation for the mass transfer coefficient in the supercritical phase (KG) is: DG (2 + 0.00187NRe0.779NSc0.546(dg0.333DG-0.667)0.116) KG ) d (2) NRe is Reynolds number defined as dVGFG/µG; d is drop diameter, VG is carbon dioxide velocity inside the precipitation vessel, FG is its density, and µG is its viscosity. The solvent mass transfer flux, NG, in the supercritical phase is the product of mass transfer coefficient and difference between its concentration at the interface between droplet and CO2 phase and its concentration in the bulk CO2 phase. Letting the latter concentration go to zero, NG ) KG(FGiyi2)

(3)



4DL πtc

)

(6)

The initial drop velocity was assumed to be the same as that of the solution exiting the nozzle.12 The carbon dioxide mass transfer flux, NL, in solvent phase (droplet) is given by the following equation: NL ) KL(FiLxi1 - FLx1)

(7)

x1i

and x1 are mole fractions of carbon dioxide at the interphase and in the droplet, respectively. x1i and y2i (interface CO2 and solvent mole fractions) were obtained for the CO2-DCM system,14 and a linear temperature relation was used for presures below mixture critical pressure. A constant interface mole fraction was used for presures above mixture critical pressure. The mole fraction was obtained from the vapor-liquid equilibrium diagram of the CO2-DCM system.14 The total number of moles, Ntotal, after one time interval, ∆t, is: Ntotal ) No + (NL - NG)πd2∆t

(8)

No is the initial number of moles in the droplet, and ∆t is the time interval. Drop diameter was calculated on the basis of the total number of moles in the droplet:

y2i is the mole fraction of solvent at the interphase. The mass transfer coefficient in the liquid phase, KL, can be calculated by Higbie’s penetration theory: KL )

(5)

o

d)

[

6Ntotal πFL /Mmixture

]

1/3

(9)

Mmixture is the mixture molecular weight.

(4)

DL is liquid diffusivity, and tc is characteristic time calculated as the ratio of drop velocity to drop diameter.

Solute Solubility Mukhopadhyay and Dalvi9 reported a new way to find solute solubility in a ternary mixture. They defined ((1 - X1)Vj2)/(V)

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as the solvent PMVF (partial molar volume fraction), where X1 is the mole fraction of carbon dioxide in droplet on solute-free basis, Vj2 is the partial molar volume of the solvent, and ν is the solvent-antisolvent mixture molar volume. With increasing CO2 mole fraction, PMVF decreases leading to decrease in solute solubility. They showed that the mole fraction of the solute can be calculated by the following equation: x3(T, P) V2(T, P, X1) (1 - X1) V(P, X1)

)

x30(T, P0) V2(T, P0, X10) (1 - X10) V(P0, X10)

(10)

V2 ) V + X1

dV dX2

(11)

The expression for solubility mole fraction for polymer (represented by x4) in ternary polymer-solvent-CO2 is given by an expression similar to eq 10. x4(T, P) (1 - X1)

V2(T, P, X1) V(P, X1)

)

x40(T, P0) (1 - X10)

V2(T, P0, X10) V(P0, X10)

pressed as mole fraction, x*3 ) at the same temperature and pressure conditions: s)

(12)

Four-component solubility mole fractions of solute and polymer can be calculated from their respective three-component values as follows: x34C ) x3(1 - x44C)

(13)

x44C ) x4(1 - x34C)

(14)

x3 x*3

(17)

The critical radius of nuclei rc depends on molecular volume of solute, Vm, Boltzmann’s constant, K, supersaturation, s, and temperature, T, as follows: rc )

x3 ) X3(1 - x1) and x1 ) X1(1 - x3); x3 is the mole fraction of solute in ternary system; T and P are operating temperature and pressure; x1 and x2 are carbon dioxide and solvent mole fractions in droplet; X3 is solute (cholesterol) solubility in solvent on CO2free basis at T and P (similarly X4 is for polymer); x30 is the solute solubility expressed as mole fraction at reference pressure P0; and X10 is the CO2 solubility on solute-free basis at P0. Solute solubility has been neglected in the CO2 phase as the pressure used is relatively lower to dissolve any considerable solute in SC CO2. The partial molar volume, Vj2, can be found from the Gibbs-Duhem equation:

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2σ3Vm KT ln s

(18)

Nucleation will proceed only if nuclei radius is larger than critical radius. The homogeneous nucleation rate, J, is the number of nuclei produced per unit volume per unit time, and it depends on supersaturation, s, nonlinearly:

(

J ) A exp -

B (ln s)2

)

(19)

A ) θRcVsN2((2σ)/(kT))0.5, N ) FMx*3 NA, and B ) (16πσ3Vs2)/ (3K3T3), where NA ) Avogadro’s number, FM ) molar density, θ is a nonisothermal factor set to 1, Rc ) condensation coefficient ) 0.1, σ ) surface tension at solid-liquid interphase, x*3 ) solute solubility expressed as mole fraction, and Vs ) solute molar volume. Mass of solute, mppt, precipitated from the droplet due to nucleation and growth in time ∆t can be determined by the following equation: mppt ) J

πd3c Fc πd3 ∆t 6 6

(20)

d is droplet diameter, and dc is critical nuclei diameter. Secondary nucleation rate, Js, also depends nonlinearly on supersaturation:

(( ))

Js ) As exp -

Bs

1/2

(ln s)2

(21)

As soon as the nuclei form, they begin to grow. Growth is a mass transfer process, and it could be characterized by a mass transfer coefficient:

Solving, 4C

x3

Ng ) KS-L(Fcx3* - Fcx3)A∆t/Mmol

x3(1 - x4) ) 1 - x3x4

(15)

x4(1 - x3) 1 - x3x4

(16)

x44C )

x34C and x44C are four-component solute and polymer solubility, respectively. The cholesterol solubility in the solvent gets affected by polymer. It has been considered that the presence of polymer decreases the solubility of cholesterol by 2 orders of magnitude because of an enhanced antisolvent effect on cholesterol than the polymer. Supersaturation, Nucleation, and Growth of Particles During the SAS process, as CO2 enters the drop and solvent departs, the solvent becomes supersaturated with the solute. Small nuclei of the solute form, which grow and finally precipitate. Supersaturation, s, is defined as the ratio of actual solute concentration (mole fraction, x3) to its solubility (ex-

(22)

Ng is the number of moles of solute transferred, KS-L is the mass transfer coefficient of solid in solvent, Fc is the solid particle density, x3* is the equilibrium mole fraction of solid, x3is the actual mole fraction of solid in the solution, A is the area on which solid is being deposited, Mmol is molecular weight of solute, and ∆t is the time interval. KS-L can be estimated by a simple relation: Sherwood number or KS-Ldc/D ) 2 D is the diffusivity of solute in solvent, and dc is the characteristic length taken as critical nuclei diameter. Use of the above relation is justified because of negligible convection in the droplet. Method of Computation Computations were carried out using MATLAB version 7 in the following sequence:

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Table 2. Property Values Used in the Model Equations 1, 2, 5, and 6 (Diffusivities are at 308 K and 75 bar) properties X3 X4 DG (m2/s) DG0 (m2/s) DL0 (m2/s) µ (Pa · s) σ (N/m) D (m2/s)

DCM

SC CO2

cholesterol

PLA

0.0482 4.7 × 10-8 4.6 × 10-9 4.2 × 10-8 4.0 × 10-4 at 318 K 5 × 10-5

0.000073

2.0 × 10-5 at 313 K 0.02 10 × 10-12

0.0075 10 × 10-12

(1) All conditions (temperature, pressure, etc.) and properties (nozzle diameter, the initial velocity, etc.) were given as input, and initial drop diameter was calculated. (2) In each time interval (∆t ≈ 10-3-10-4 s), diffusivity (from values DG0 and DL0 listed in Table 2 and using eq 8), density (from Peng-Robinson equation of state), mass transfer coefficient, mass fluxes, total number of moles, solute solubility, and drop diameter were calculated. Time steps lower than those indicated did not change the results significantly. Also, the Span and Wagner18 equation of state is excellent for CO2 property calculations. However, the equation contains many terms and parameters to be calculated. Predictions of Peng-Robinson equation of state (PREOS) compare well with those of Span and Wagner. For liquid CO2, density predictions are nearly the same for the two equations (∼+2% deviation of PREOS from Span-Wagner at 30 °C). For gaseous CO2, the predictions differ considerably at lower temperatures. Yet as temperature increases, the difference reduces. For example, at 30 °C, density calculated by PREOS is about 11% higher than that calculated by the Span and Wagner equation. At 40 °C and 80 bar, however, the difference between the two predictions falls to about 2%. In the current work, the difference between the density predictions is expected to be less (about 2%) because temperatures exceed 40 °C and pressure is about 90 bar. The diffusivity of PLA for the system studied is not reported in the literature. Diffusivity of PLA, because of its higher molecular weight, would be lower than that of cholesterol. Also, it would change during the process, being high during the initial stages of evaporation and low during the later stages. For the sake of simplicity, diffusivities of cholesterol and PLA were assumed to be the same. For encapsulation, diffusivity of PLA is unimportant because PLA does not grow but precipitates on the already precipitated cholesterol particles. For coprecipitation, smaller particles of PLA would form if a lower value is taken for its diffusivity. The mechanisms proposed and explained in the current work do not change if PLA diffusivity is lowered. (3) The homogeneous nucleation rate has been used for cholesterol micronization in three- and four-component systems. Heterogeneous secondary nucleation rate has been used for polymer in the four-component system (coprecipitation and encapsulation modeling). Values of A for primary nucleation can be determined by the equation provided after eq 19. The following typical values were taken for the parameters in primary and secondary nucleation rates: B ) 1000, As ≈ 1020, and Bs ) 100. The rate of nucleation given by eq 19 is for industrial crystallizers, where the number of particles formed is quite large. However, in the present work, the particle size distribution in the SAS process has been estimated from the rate of supersaturation attained in a single droplet. In view of the fact that the number of particles formed in a droplet (the initial size being about 50 µm) is too small to be used for finding their size distribution, a large number of drops should be considered to be able to estimate the particle sizes and their

distribution. This was indirectly achieved by fixing the value of B, as given above, to obviate the problem, that is, to obtain a reasonable number of particles and for making subsequent calculations of growth. It is to be noted that the values of A and B do not affect the critical radius of the nuclei (eq 18), particle size (eq 20), and the particle size distribution. It only changes the total number of particles. The nucleation rates with the changed value of B are about the same order of magnitude as those in industrial crystallizers. The values for A and B for secondary nucleation are not available in the literature. They are reported to be much smaller and not of any significance. Hence, the values fixed for A and B, for both primary and secondary nucleation, do not affect the results on particle size and distribution in the present work, that is, for understanding of the mechanism of coprecipitation of two solutes or encapsulation of one solute with the other and for estimating the particle sizes and their distribution. Growth has been quantified by a mass transfer equation with the difference in mole fraction as the driving force. Supersaturation, nucleation, nuclei growth, and solute precipitation were calculated by the equations presented earlier. A growth matrix that tracks the change in particle diameter in each time interval is made. This matrix can be expressed as follows:

(

0 0 0 0 t1 rc1 0 0 rc1 + rg1 rc2 t2 0 t3 rc1 + rg1 + rg1 ′ rc2 + rg2 rc3 . . . . . . . . tn . . .

0 0 0 0 . . .

0 0 0 0 . . .

.. .. .. .. .. .. ..

0 0 0 0 . . .

)

In the above matrix, the first column indicates time, and all other columns indicate the particle radius. The symbol rc indicates critical nuclei radius at a specific time t, and rg indicates increase of radius by particle growth. At time t1, n1 number of nuclei are formed with a critical radius of rc1; at t2, they will grow to rc1 + rg1 and n2 number of new nuclei will form with critical radius rc2; at t3, the particles that formed at t1 will grow further to rc1 + rg1 + rg1 ′ and those that formed at t2 will grow to rc2 + rg2. The critical radius changes from time to time as the supersaturation changes. This procedure is continued until all the solvent evaporates. Similar to the growth matrix, a particle number matrix can be expressed to track the number of particles as a function of time.

(

0 t1 t2 t3 . . tn

0 n1 n1 n1 . . n1

0 0 n2 n2 . . n2

0 0 0 n3 . . n3

0 0 0 0 . . .

0 0 0 0 . . .

.. .. .. .. .. .. ..

0 0 0 0 . . nn

)

(4) The equations were solved until all of the solvent evaporates and the total process time will be tn, which corresponds to the last row of the matrices. Results and Discussion Supersaturation, Nucleation, and Growth of Particles in One-Solute Systems. Figure 4a-f illustrates predictions of performances of several steps occurring in a drop during precipitation of cholesterol particles from it by the SAS process. The drops were generated from a solution containing 0.1 mol

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Figure 4. Concentration of CO2 and cholesterol in the drop and precipitation of cholesterol as a function of time. (a) CO2 mole fraction inside droplet versus time, (b) cholesterol solubility expressed as mole fraction in DCM versus CO2 mole fraction inside droplet, (c) cholesterol mole fraction in droplet versus time, (d) DCM moles in droplet versus time, (e) nucleation rate of cholesterol versus time, and (f) precipitated cholesterol moles versus time. Operating conditions were 40 °C, 82 bar, CO2 flow rate was 50 kg/h, solution flow rate was 0.5 kg/h, and initial concentration of cholesterol in the solution was 0.1 mol %.

Figure 5. Effect of initial concentration of cholesterol on supersaturation and particle size distribution of cholesterol. Operating conditions were 40 °C, 82 bar, CO2 and solution flow rates were 50 kg/h and 0.5 kg/h, respectively. (a) Supersaturation versus time; (b) particle size distribution.

% cholesterol, which was sprayed in a vessel through a 100 µm nozzle at a rate of 0.5 kg/h. Supercritical CO2 flowed into the vessel at 50 kg/h; both the solution and CO2 were at 313 K. Figure 4a shows that the CO2 mole fraction rises rapidly in the drop to about 0.9 within 0.05 s. Consequently, cholesterol solubility falls, the antisolvent effect of CO2 (Figure 4b). In fact, the solubility becomes vanishingly low at mole fractions of CO2 greater than 0.9. Figure 4c shows that mole fraction of cholesterol falls precipitously initially as CO2 diffuses rapidly and stays constant for some time and then falls to almost zero. The amount of solvent decreases gradually; the time for it to reach zero, about 0.8 s, could be considered as the process time (Figure 4d). Figure 4e shows that nucleation rate of cholesterol rises quickly, peaks, and then falls drastically. Supersaturation of cholesterol is low initially due to its higher solubility, and the nucleation rate is lower. As the solubility is lowered, supersaturation and hence the nucleation rate rise. Eventually, the mole fraction of cholesterol in the droplet falls, lowering the supersaturation and the nucleation rate. The nucleation ends at about 0.2 s after which the nucleated particles grow for about

0.6 s. Precipitation rate of cholesterol is high until nucleation ceases; later, the rate falls dramatically as the particles grow (Figure 4f). Effect of Operating Conditions on Processes. Figure 5a and b shows that, when the solution containing more solute is sprayed, the resultant drop becomes supersaturated earlier, and supersaturation levels (plotted as logarithm of supersaturation) are higher. When the drop contains more solute, high supersaturation levels are maintained for a shorter period during which nuclei are generated and the particles grow over the remaining long period of time. The net effect is that larger particles form and their sizes are distributed over a wide range. When the drop contains less solute, supersaturation is high for a longer period, more nuclei form, and they grow for a shorter period resulting in smaller particles with a narrower size distribution. Figure 6a and b shows that at higher CO2 flow rates, higher supersaturation levels for shorter period lead to formation of more particles with a narrower size distribution. A similar effect is shown in Figure 7a and b at higher pressures. Increase in pressure causes supersaturation to increase and

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Figure 6. Effect of CO2 flow rate on supersaturation and particle size distribution of cholesterol. Operating conditions were 40 °C, 82 bar, and initial cholesterol concentration in the solution was 0.5 mol %. (a) Supersaturation versus time; (b) particle size distribution.

Figure 7. Effect of pressure on supersaturation and particle size distribution of cholesterol. Operating conditions were 40 °C, initial cholesterol concentration in the solution was 0.5 mol %, and CO2 and solution flow rates were 50 and 0.5 kg/h, respectively. (a) Supersaturation of cholesterol versus time; (b) particle size distribution.

Figure 8. Supersaturation of cholesterol and PLA versus time. Operating conditions were 45 °C and 90 bar, respectively. (a) Supersaturations at a weight ratio of PLA and cholesterol of 2:1. Concentrations of PLA and cholesterol in the solution sprayed were 0.5 and 0.24 wt %, respectively. (b) Supersaturations at a weight ratio of PLA and cholesterol of about 1:6. Concentrations of PLA and cholesterol in the solution sprayed were 0.58 and 2.9 wt %, respectively.

the process time (complete solvent evaporation time) to decrease. This is due to a higher CO2 solubility inside droplet at higher pressure. Supersaturation, Nucleation, and Growth of Particles in Two-Solute Systems. In the section on experimental results, it was shown that PLA encapsulated cholesterol when the weight ratio of the former to the latter in the sprayed solution was high (Figure 2e and f). It was also shown that they coprecipitated when the ratio was low (Figure 2c and d). These phenomena can be explained by their supersaturation behavior. Figure 8a shows that, when the ratio was low, cholesterol supersaturation becomes high rapidly, stays nearly constant until about 0.025 s, falls until about 0.05 s, and then plateaus. Until the supersaturation is high, the solution gets depleted of cholesterol mainly due to nuclei formation rather than their

growth. When the supersaturation is low, nucleation rates are low, and the solution gets depleted of cholesterol mainly due to growth of the nucleated particles and few new nuclei are created. Supersaturation of PLA rises slowly and becomes comparable to that of cholesterol at about 0.04 s. More nuclei of PLA than cholesterol are formed at this time, and their number keeps growing until the end of the process. Because nuclei of both cholesterol and PLA form during the process, they coprecipitate. Figure 8b shows that, when the ratio was high, the supersaturation of cholesterol becomes high and remains constant for longer duration than in Figure 8a. This means that the nucleation rates are high for longer time and more nuclei are generated. PLA supersaturation is low for most of the time and becomes considerable only at the end of the process. Most of

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Figure 9. Nucleation rates and particle size distribution of cholesterol and PLA. Operating conditions were 45 °C and 90 bar, initial concentrations of cholesterol and PLA were 0.24 and 0.5 wt %, respectively. CO2 flow rate was 50 kg/h, and ratio of mass flow rates of CO2 to that of solution was 90. (a) Nucleation rate of cholesterol versus time, (b) nucleation rate of PLA versus time, (c) particle size distribution of cholesterol, and (d) particle size distribution of PLA.

Figure 10. Particle size distribution before and after encapsulation. Operating conditions were 45 °C and 90 bar, initial concentrations of cholesterol and PLA were 0.7 and 1.4 wt %, respectively. CO2 flow rate was 50 kg/h, and ratio of mass flow rates of CO2 to that of solution was 90. (a) Before encapsulation; (b) after encapsulation.

the cholesterol would have nucleated and grown by the time PLA supersaturation became high. Hence, when PLA precipitates, it deposits on the already precipitated cholesterol particles, leading to encapsulation. Growth of PLA on cholesterol rather than secondary nucleation leads to encapsulation. If PLA saturation becomes high almost at the end of the process, then it precipitates on the already formed cholesterol particles and encapsulates them; if the saturation becomes high during the process, then PLA particles coprecipitate and

encapsulate as well. Hence, in addition to ratio of PLA and cholesterol, conditions that reduce time of the process, such as higher CO2 flow rate and temperature, lead to encapsulation. On the other hand, conditions that make the time for evaporation of the solvent longer result in coprecipitation. Our experiments show an encapsulation efficiency of about 32%; that is, one-third of PLA was encapsulated and twothirds was not. Thus, in the experiments, PLA attained a high supersaturation before all the solvent evaporated.

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The size distribution of encapsulated particles can be estimated as follows: Assume that Nparticles of cholesterol are produced by nucleation and growth and no PLA has deposited on them. If the diameters of cholesterol particles, before and after encapsulation, are d1 and d2, respectively, then material balance for PLA gives Mpolymer 1 π(d32 - d31)Fpolymer ) 6 Nparticles or d2 )

(

)

Mpolymer 1 6 x x + d31 Nparticles Fpolymer π

1/3

(23)

Mpolymer is the mass of the polymer in the feed, and Fpolymer is the density of the polymer. In writing eq 23, it is assumed that an equal amount of PLA precipitates on all cholesterol particles. Therefore, the size of smaller particles rises far more than those of bigger ones, resulting in uniform size of encapsulated particles. Figure 9 shows the nucleation rate and particle size distribution of both cholesterol and PLA corresponding to the operating conditions in Figure 8b. The nucleation rate of cholesterol is 104 times higher than that of PLA (Figure 9a and b). Lower PLA nucleation rate indicates that few of its nuclei form. Figure 9c and d shows that the number of cholesterol particles produced is high and practically no PLA particles form. This indicates that PLA particles do not coprecipitate but encapsulate the grown cholesterol particles. Figure 10a shows a wide particle size distribution of cholesterol particles before encapsulation for conditions corresponding to Figure 9b. Once the particles are encapsulated with PLA, the distribution becomes uniform (Figure 10b), a fact observed in experiments. Conclusions Coprecipitation and encapsulation of cholesterol particles with PLA from their solutions in DCM have been studied by experiments and mathematical modeling. Formation of small cholesterol particles was studied with solutions of cholesterol in DCM. The model equations included nuclei formation and their growth for both cholesterol and PLA. In systems containing one solute, the model predicts that higher pressures, higher CO2 flow rates, and lower solute fractions lead to smaller particles with narrower distribution. When the PLA weight fraction was significantly higher than cholesterol in the feed solution, smaller, spherical particles were produced, and PLA encapsulated cholesterol. When PLA content was lower, larger, needle-shaped particles were produced; also, PLA and cholesterol coprecipitated. The model results gave an insight into the mechanisms by which either coprecipitation or encapsulation occurs. If PLA supersaturation becomes high at the end of the process, it encapsulates the precipitated cholesterol particles by growing on them. It coprecipitates, if it attains high supersaturation during the process.

Acknowledgment We wish to thank Yogesh Kadam for his valuable help in conducting experiments on the pilot plant. Literature Cited (1) Wang, Y.; Dave, R.; Pfeffer, R. Polymer Coating/Encapsulation of Nanoparticles Using a Supercritical Anti-Solvent Process. J. Supercrit. Fluids 2004, 28, 85. (2) Martin, T. M.; Bandi, N.; Shulz, R.; Roberts, C. B.; Kompella, U. B. Preparation of Budesonide and Budesonide-PLA Microparticles Uusing Supercritical Fluid Precipitation Technology. AAPS PharmSciTech 2000, 3, 18. (3) Diego, Y.; Pellikaan, H. C.; Wubbolts, F. E.; Witkamp, G. J.; Jansens, P. J. Operating Regimes and Mechanism of Particle Formation During the Precipitation of Polymers Using the PCA Process. J. Supercrit. Fluids 2005, 35, 147. (4) Charbit, G.; Boutin, O.; Badens, E.; Carretier, E. Co-precipitation of a Herbicide and Biodegradable Materials by the Supercritical Anti-Solvent Technique. J. Supercrit. Fluids 2004, 31, 89. (5) Kim, M.; Lee, S.; Park, J.; Woo, J.; Hwang, S. Micronization of Cilostazol Using Supercritical Anti-Solvent (SAS) Process: Effect of Process Parameters. J. Powder Technol. 2007, 177, 64. (6) Chen, K.; Zhang, X.; Pan, J.; Zhang, W.; Yin, W. Gas Anti-Solvent Precipitation of Ginkgo Ginkgolides with Supercritical CO2. J. Powder Technol. 2005, 152, 127. (7) Reverchon, E.; Porta, G. D.; Falivene, M. G. Process Parameters and Morphology in Amoxicillin Micro and Submicro Particles Generation by Supercritical Anti-Solvent Precipitation. J. Supercrit. Fluids 2000, 17, 239. (8) He, W. H.; Suo, Q. L.; Jiang, Z. H.; Shan, A.; Hong, H. L. Precipitation of Eephedrine by SEDS Process Using a Specially Designed Prefilming Atomizer. J. Supercrit. Fluids 2004, 31, 101. (9) Mukhopadhyay, M.; Dalvi, S. V. Partial Molar Volume Fraction of Solvent in Binary (CO2-Solvent) Solution for Solid Solubility Predictions. J. Supercrit. Fluids 2004, 29, 221. (10) Werling, J. O.; Debenedetti, P. J. Numerical Modeling of Mass Transfer in Supercritical Anti-Solvent Process. J. Supercrit. Fluids 1999, 16, 167. (11) Lora, M.; Bertucco, A.; Kikic, I. Simulation of Semicontinuous Anti-Solvent Recrystallization Process. Ind. Eng. Chem. Res. 2000, 39, 1487. (12) Mukhopadhyay, M.; Dalvi, S. V. Mass and Heat Transfer Analysis of SAS: Effects of Thermodynamic States and Flow Rates on Droplet Size. J. Supercrit. Fluids 2004, 30, 333. (13) Mukhopadhyay, M.; Dalvi, S. V. Analysis of Supersaturation and Nucleation in a Moving Solution Droplet with Flowing Supercritical Carbon Dioxide. J. Chem. Technol. Biotechnol. 2005, 80, 445. (14) Diego, Y.; Wubbolts, F. E.; Jansens, P. J. Modelling Mass Transfer in the PCA Process Using the Maxwell-Stefan Approach. J. Supercrit. Fluids 2006, 37, 53. (15) Taki, S.; Badens, E.; Charbit, G. Controlled Release System Formed by Supercritical Anti-Solvent Coprecipitation of a Herbicide and a Biodegradable Polymer. J. Supercrit. Fluids 2001, 21, 61. (16) Mugele, R. A. Maximum Stable Droplets in Disperoids. AIChE J. 1960, 6, 3. (17) Hughmark, G. A. Liquid-Liquid Spray Column Drop Size, Holdup and Continuous Phase Mass Transfer. Ind. Eng. Chem. Fundam. 1967, 6, 408. (18) Span, R.; Wagner, W. A New Equation of State for Carbon Dioxide Covering the Fluid Region from the Triple-Point Temperature to 1100 K at Pressures up to 800 MPa. J. Phys. Chem. Ref. Data 1996, 25, 1509.

ReceiVed for reView July 7, 2010 ReVised manuscript receiVed November 1, 2010 Accepted November 19, 2010 IE101449A