Formation of Composite Crystals by Precipitation in Supercritical CO2 Boris Y. Shekunov,*,† Simon Bristow,‡ Albert H. L. Chow,§ Lachlan Cranswick,| David J. W. Grant,⊥ and Peter York†,‡
CRYSTAL GROWTH & DESIGN 2003 VOL. 3, NO. 4 603-610
Drug Delivery Group, School of Pharmacy, University of Bradford, Bradford BD7 1DP, United Kingdom, Bradford Particle Design Limited, 69 Listerhills Science Park, Campus Road, Bradford BD7 1HR, United Kingdom, School of Pharmacy, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong SAR, China, CLRC Daresbury Laboratory, Daresbury, Warrington, Cheshire WA4 4AD, United Kingdom, and Department of Pharmaceutics, College of Pharmacy, University of Minnesota, Weaver-Densford Hall, 308 Harvard Street Southeast, Minneapolis, Minnesota 55455-0343 Received February 14, 2003;
Revised Manuscript Received May 2, 2003
ABSTRACT: Acetaminophen (A) and p-acetoxyacetanilide (PAA) were used as model drug substances to study purification and coformulation of structurally similar molecules by crystallization from supercritical CO2. Incorporation of PAA into the crystal structure of A was defined by the mutual solubility of crystals of both molecules according to their different solvent-solute interactions, by the thermodynamics of the A-PAA solid solution phase, and by the kinetics of crystallization reflected by the specific surface interactions. The interaction between PAA and A resulted in significant changes to the crystal bulk and surface free energy, particle size, and morphology. Accurate determination of the lattice constants revealed the formation of a secondary A-PAA phase with a deformed crystal lattice. The observed changes in the thermal behavior of the resulting solid solutions are explained mainly by changes of the entropy of the solid phase with smaller changes in enthalpy and even smaller elastic energy contributions. Introduction Crystallization or precipitation of an active drug or excipient is the most general method for the separation or purification stage following the chemical synthesis of a pharmaceutical compound. In addition, coprecipitation or coformulation can be considered complementary to purification, where modification of the solid-state properties of the product and distribution of the ingredients are defined by the solubilities and precipitation kinetics. An important practical case is that of structurally similar compounds, for example, reaction byproducts, chiral molecules, additives, and impurities. The similarity of their molecular structures ensures that these compounds strongly interact with each other. Formation of solid solutions may be expected in this case. Strong solid-solid intermolecular interactions typically result in separation problems and in significant variations of the solid-state and particulate properties. The present study examines a model system, p-acetoxyacetanilide (PAA) plus p-hydroxyacetanilide (acetaminophen, A, paracetamol). PAA is a synthetic precursor of A and is structurally similar to A. PAA has also been suggested as a prodrug of A.1 The acetyl group, -COCH3, chemically discriminates PAA from A. Chow and Grant2 showed a strong modifying effect of PAA on the properties of A crystals in aqueous solution, while Shekunov et al.3 investigated in some detail the surface growth kinetics of A. * Corresponding author. E-mail:
[email protected]. † University of Bradford. ‡ Bradford Particle Design Limited. § The Chinese University of Hong Kong. | CLRC Daresbury Laboratory. ⊥ University of Minnesota.
The present work investigates the antisolvent precipitation process using supercritical (sc) carbon dioxide (scCO2). The advantages of using scCO2 are defined by two major factors. First, scCO2, being a compressed gas, can be efficiently separated from both organic cosolvents and solid products, allowing clean, one-step, recyclable processing. Second, the solvent power of scCO2 can be controlled within a wide solubility range by adjusting both pressure and temperature. The latter property, well-known for sc fluid extraction, is also utilized in the area of selective precipitation, separation of impurities, and control of solid forms. Most research on coprecipitation with sc fluids has focused on production of polymer-drug particles for controlled or sustained drug release4-6 (e.g., physical mixtures of powders have been obtained using the technique of rapid expansion of supercritical solutions (RESS)).7,8 Physical mixtures (microcomposites) of pharmaceutical compounds, such as acetaminophen, ascorbic acid, urea, and chloramphenicol, have also been obtained using antisolvent precipitation, and the effect of pressure on the separation of these drugs has also been investigated.9 However, few, if any, systematic studies have focused on the mechanism of precipitation, which results in the formation of a solid solution in such systems, or on the effect of processing conditions on the surface and solid-state properties of the solids obtained. The crystallization process of pure A in scCO2 has been studied in our previous work.10-12 The three aims of the present work are first, to investigate the precipitation of A in the presence of PAA as an additive in the supercritical fluid phase; second, to determine the effect of PAA on the solid-state and particulate properties of the materials obtained; and third, to define the general crystal-
10.1021/cg034026o CCC: $25.00 © 2003 American Chemical Society Published on Web 05/21/2003
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lographic and thermodynamic characteristics of the solid solutions produced. Materials and Methods Chemicals and Reagents. A used in all experiments had purity >99% (Sigma Chemicals, Poole, UK). PAA was prepared from A by acetylation13 and was purified by recrystallization. Acetonitrile, ethanol, and isooctane (2,2,4-trimethylpentane) were of analytical grade (AnalaR, BDH Chemicals, Poole, UK). Monosodium phosphate (SigmaUltra grade) was supplied by Sigma Chemicals (Poole, UK). All liquid probes used in inverse gas chromatography (IGC) were of analytical grade (Labscan, Dublin, Ireland). Carbon dioxide was Food Grade (BOC, Manchester, UK). Precipitation Process. Solutions of PAA and A in ethanol were typically 2% (w/v). The mol % of PAA (relative to A) in the solution (Csolution) was varied between 0.8 and 8%. Solutions were processed using the (SEDS) technique as described previously.12 This process involved co-introduction of ethanol solution and supercritical CO2 into a coaxial mixing nozzle at flow rates of 0.1 mL min-1 (reference ethanol density 0.78 g/mL) and 9.0 mL min-1 (reference CO2 density 1 g/mL). The precipitation occurred in a 50 mL stainless steel vessel thermostated in an air-heated oven (Applied Separations, Allentown, PA). Paper filters (Schleicher & Schuell, Dassel, Germany) were inserted into the base of the vessel for particle retention. The operating pressure and temperature were each varied (90-150 bar and 40-80 °C) as described in the Results. Solubility of A and PAA in Modified CO2. Prior to the crystallization experiments, an online dynamic solubility method was used to determine the equilibrium solubility profile of PAA and A in the ethanol + CO2 mixture under the extreme experimental conditions (150 bar and 80 °C). This method was validated in our previous work14 and involved passing the ethanol + CO2 mixture (at the same composition as during precipitation) through a packed sample extraction vessel and then through a high-pressure UV flow cell. After calibration and baseline subtraction, the resulting signal was used to establish the equilibrium solute concentrations. High Performance Liquid Chromatography (HPLC). A-PAA material recovered from the vessel was analyzed in duplicate by reversed phase HPLC using mobile phase (acetonitrile/0.05 M anhydrous monosodium phosphate buffer, pH 3.0, 15/85 v/v) as the sample diluent. PAA eluted at a retention time of 4.0 min and was well-resolved from the A peak at 6.0 min. The %PAA content in the powders obtained (csolid) was calculated from the amounts of PAA and A determined by external standardization at 248 nm. Dissolution Test. A comparative analytical method was developed to distinguish between solid solutions (A-PAA) and physical mixtures of PAA and A. Mixtures of these compounds were prepared using a WAB T2C turbula mixer (Basel, Switzerland) and then analyzed by HPLC to determine the homogeneity and the percentage of PAA in the mix. A method was developed and validated to selectively extract PAA from the physical mixtures and supercritically processed powders. To validate the procedure, a 1% physical mixture of PAA (verified as 1.0044% by HPLC) and A was prepared, and three subsamples were extracted (25 °C), for which the %CV was 6.4%. For this purpose, isooctane was added to 50 mg of sample (accurately weighed in duplicate) in 5.0 mL volumetric flasks that were then inverted 50 times. The solutions were transferred to 2.0 mL polypropylene ultracentrifuge tubes and then placed in an ultracentrifuge (Model 5415, Eppendorf, Hamburg, Germany) at 5000 rpm for 3 min. Supernatant (1.5 mL) was then removed using a calibrated Eppendorf auto-pipet, and the solvent evaporated at 50 °C in a fan-assisted oven (Applied Separations). The residue was the reconstituted in 1.5 mL of HPLC mobile phase, diluted appropriately, and analyzed to quantify the total amount of PAA present in the weighed sample. SEDS samples and physical mixtures containing similar levels of PAA (0.5, 1.0, and 2.0%; exact amounts confirmed by triplicate HPLC analysis) were extracted to
Shekunov et al. provide direct comparison and to test for possible formation of solid solutions in the SEDS samples. Weighed subsamples (50 mg) were placed in 20 mL scintillation vials, and 5.0 mL of isooctane was added. The vials were gently agitated by hand and then placed in a fan-oven at 25 °C for 48 h. The solutions were decanted into centrifuge tubes and spun at 7000 rpm for 4 min. Known volumes of supernatant were removed, evaporated, and reconstituted in mobile phase for analysis by HPLC. Inverse Gas Chromatography (IGC). IGC was performed on a gas chromatograph (Series II 5890, Hewlett-Packard, Wilmington, DE) equipped with an integrator and flame ionization detector. The injector and detector temperatures were maintained at 100 and 150 °C, respectively. Glass columns (60 cm long and 3.5 mm i.d.) were deactivated with a 5% solution of dimethyldichlorosilane in toluene before being packed with A-PAA powder. The columns were plugged at both ends with silanised glass wool and maintained at 40 °C. Data were obtained for a known weight and surface area of the sample using nitrogen gas (purity >99.995%) flowing at 20.0 mL/min. The column was weighed before and after the experiment to ensure no loss of materials during the run. A trace amount of vapor from nonpolar and polar probes was injected. The retention times and volumes of the injected probes were measured at infinite dilution and thus were independent of the quantity of probe injected. The nonpolar probes employed were pentane, hexane, heptane, octane, or nonane, whereas the polar probes were dichloromethane, chloroform, acetone, ethyl acetate, tetrahydrofuran, or diethyl ether. The A-PAA powders were produced under four extreme conditions as described here. Triplicate measurements were made in separate columns. Differences in surface energetics were reflected in the calculated dispersive component of the surface free energy, γD S , which were determined from the 1/2 according to the slope of the plot of RT ln VN against (γD L) following equation: 1/2 D 1/2 RT ln VN ) 2aNA(γD + const S ) (γL )
(1)
where R is the gas constant, T is the absolute temperature of the column, a is the surface area of the probe, NA is Avogadro’s number, γD S is the dispersive component of surface free energy of A powder, and γD L is the dispersive component of surface free energy of the solvent probe. The surface free energy of adsorption of polar probes has both dispersive and specific components. The specific component of (∆GSP A ) (i.e., the surface free energy of adsorption) can be estimated from the vertical distance between the alkane reference line and the polar probes of interest. This free energy term is related to the donor number (DN) and acceptor number (AN*) of the polar solvent by the following equation:
∆GSP A ) KADN + KDAN*
(2)
DN describes the basicity or electron donor (proton acceptor) ability of a probe, while AN* defines the acidity or electron acceptor (proton donor) ability. Here, AN* denotes a correction for the contribution of the dispersive component, while the entropy contribution into the surface energy is assumed to be negligible. Thus, a plot of -∆GSP A /AN* versus DN/AN* yields a straight line for which KA and KD correspond to the slope and intercept, respectively. A more detailed theory of these measurements is discussed elsewhere.15,16 Differential Scanning Calorimetry (DSC). The calorimeter (DSC 7 module of a Perkin-Elmer 7 series Thermal Analysis System, Beaconsfield, UK) was calibrated using a pure indium standard (melting point 156.6 °C) and confirmed using zinc (melting point 419.5 °C). Samples (typically 5 mg) were accurately weighed into crimped aluminum pans. In the case of physical mixtures used for comparison with A-PAA samples and for studies of eutectics, the A and PAA powders were mixed using a T2C turbula mixer. All samples were heated at 10 °C min-1 from 100 to 200 °C.
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Table 1. Solubility of Acetaminophen, C0A, and p-Acetoxyacetanilide, C0PAA, in Pure CO2 at Various Temperatures and Pressures P (bar)/T (°C) solubility
90/40
90/80
150/40
150/80
C0A × 10-5 (mol fraction) C0PAA × 10-5 (mol fraction)
0.6 1.3
0.2 2.5
0.9 6.7
1.1 12.0
Particle Size and Shape Analysis. Scanning electron microscopy (SEM) was performed using an electron microscope (S-520, Hitachi Ltd, Tokyo, Japan). Dry powder samples were attached to aluminum SEM stubs using self-adhesive carbon disks and were subsequently sputter-coated with a conducting gold layer (K550 Sputter Coater, Emitech, Ashford, UK). The SEM images were captured using suitable software (I-Scan100, ISS Group Services, UK), viewed, and photographed under a range of magnifications. The time-of-flight measurements were performed using an AeroSizer (TSI Inc., Minneapolis, MN) with an AeroDisperser (TSI). The mean volume particle diameter, dV, was calculated from the measured particle size distribution. The shear force in the disperser was set to the maximum (3.4 psi), deaggregation to high and the feed rate to low to facilitate production of primary particles. The reproducibility, defined by the deviations in all particle size classes, was checked by triplicate measurements and was within 11%. High-Resolution X-ray Powder Diffractometry. Highresolution powder diffractometry was used to determine the characteristic diffraction peaks of A and to distinguish crystallographic changes (peak shift and peak broadening) of A-PAA composites. The experiments were carried out at the Synchrotron Radiation Source (SRS, station 2.3, Daresbury Laboratory, Warrington, UK). The X-ray wavelength, λ, was 1.3997 Å. The diffractometer had a flat-plate/parallel foils HartParrish geometry and was calibrated with an accuracy of 10-4° using the diffraction peaks of crystalline silicon. All samples were placed in rotating plate holders and scanned from 3 to 40° 2ϑ with a resolution of 0.01° and a typical signal integration time of 1 s. The diffraction data of A-PAA samples were corrected for the beam decay. In addition, the relative beam intensity during all measurements was validated using a standard sample of highly crystalline A powder. First, the exact position of several characteristic diffraction peaks, the integral breath, β, and the Full Width at Half Maximum (fwhm) of the pseudo-Voigt function were determined using the peak fitting option of the program ORIGIN. An attempt was then made to analyze the physical diffraction line broadening caused by distribution of domain size and strain in particles as described17 using the program POWDER CELL18 and applying the whole profile Le Bail fitting option of this software. The instrument broadening fwhm was assumed to be 0.025°, which is typical for an SRS diffractometer.19 However, the preliminary results showed the presence of peak broadening and peak asymmetry consistent with at least two different phases in the A-PAA samples rather than broadening caused by crystal defects17 in a single phase. This effect was modeled as two idealized end-member phases, using the software, structureless whole-profile Le Bail20 fittingoption of LHPM-Rietica for Windows.21 Such analysis involved insertion of the space group and rough cell constants of the end phases and slowly releasing the refineable parameters as part of the least squares refinement until the best visual fit to the data was achieved using a pseudo-Voigt function with asymmetry correction. The varied parameters included shifted Chebyshev background, 2θ offset, unit cell (U,V,W) width, γ-1,2 shape, and peak asymmetry. Modeling of a two-phase composition using Rietveld analysis based on a literature structure of A22 provided the quantitative determination of these two phases in the solid solution, A-PAA.
Results Particle Formation. Table 1 gives the equilibrium solubility of A and PAA pure substances at selected
Figure 1. Dependence of the PAA content in the solid phase, cPAA, on the concentration of additive in solution, cPAA, at various pressures and temperatures.
pressures and temperatures. Under all conditions, the solubility of PAA is greater than that of A, and in particular, by an order of magnitude at 80 °C. As a result, PAA did not precipitate as a separate solid phase at the relatively low solution concentrations, 1.9 mol %) in the coprecipitated material (A-PAA), no separate melting peak was detected. Table 2 contains the thermodynamic data complementary to Figure 2, which shows a significant reduction of ∆Hf, from 180.9 J/g for the highly crystalline reference material to 138.1 J/g for the A-PAA sample obtained at 90 bar and 80 °C, whereas the melting temperature changes less significantly. Comparison between Figures 4a and 5 demonstrates that ∆H is much greater for the coprecipitated materials than for the physical mixtures at the same composition. Therefore, the observed reduction of the fusion enthalpy, ∆Hf, and increase of the fusion entropy, ∆Sf ) ∆Hf/Tm, are related more to disorder in the crystal lattice of A than to the chemical interactions between the A and the PAA molecules. However, it is theoretically possible that PAA might have precipitated as a separate amorphous phase leading to the decrease of the overall value of ∆Hf. To test this possibility, an analytical method employing selective dissolution was developed. The results in Table 3 indicate that the composition of the material extracted from the precipitated sample is close to that in the solid phase, whereas the dissolution rate of PAA in the physical mixtures is several times greater than that in the precipitated A-PAA samples. These data confirm that A and PAA molecules form a homogeneous solid solution during precipitation. More detailed information on the longrange ordering was obtained from the crystallographic analysis presented below.
Figure 6. Characteristic diffraction peaks (021) and (220) of pure A obtained under conditions of 150 bar, 40 °C (broken line), 90 bar, 80 °C (thin solid line), and of A-PAA (1.9 mol % PAA) obtained at 90 bar, 80 °C (thick solid line).
Crystal Structure of the A-PAA Solid Solution. Comparison of the major diffraction peaks (Figure 6) indicate a wide peak broadening for A-PAA samples. This broadening is particularly clear for the samples obtained at high temperature/low-pressure conditions (i.e., 90 bar and 80 °C). The diffraction intensity also decreased noticeably for these materials. Quantitatively, these differences can be expressed through the changes of the integral breadth, β ) A/I, defined as the width of the rectangle having the same area, A, and intensity, I, as the observed line profile. For example, β (021) increases from 0.052 to 0.072 with addition of PAA. The incorporation of PAA molecules into the crystal structure of A caused a significant and systematic shift of the diffraction peaks of the order ∆(2ϑ) = 0.01° toward smaller angles (Figure 6). This shift corresponds to an average relative increase of d-spacing, ∆d/d = 0.5% and to a corresponding increase of crystal volume, ∆V/V = 0.3% for samples crystallized at 90 bar and 80 °C and with 8 mol % of PAA in solution. Assuming that the reference sample of A has 100% crystallinity, the crystallinity of other samples may be defined on the basis of combined area of the major diffraction peaks (Figure 6). Then, the crystallinity equals 80% for pure A precipitated at 90 bar and 80 °C, whereas it equals 52% for the sample precipitated under the same conditions but with 8 mol % of PAA in solution. More comprehensive structural analysis was obtained using Le Bail fitting with two end phases having different cell parameters, of which one is the major A phase and the other is the minor phase, composed of a deformed A unit cell with incorporated PAA molecules. A satisfactory Rietveld fitting between the theoretical and the experimental data was obtained using this approach. The resulting profile pattern analysis and data given in Table 4 show that the peak spreading was consistent with expansion of the solid solution phases primarily in the b axis direction, to accommodate the longer PAA molecule within the original A crystal structure. This quantitative phase analysis indicates that the amount of the solid solution of A in PAA (minor A-PAA phase) has the same order of magnitude, but is approximately twice as large, as the amount of PAA incorporated as the additive.
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Table 4. Results of the Two-Phase Le Bail Unit Cell Refinement of the A-PAA Material Obtained at a Pressure of 90 Bar and Temperature of 80 °C as Compared to the Pure A Obtained at 150 Bar and 40 °Ca cPAA (mol %) 1.9
0 a
phase
x (mol %)
a (Å)
b (Å)
c (Å)
β (deg)
95.94 (1.51 4.06 (0.36 100
12.8870 (0.0003 12.898 (0.001 12.8715 (0.0002
9.3798 (0.0001 9.4125 (0.0008 9.3683 (0.0001
7.0987 (0.0002 7.0879 (0.0003 7.0942 (0.0001
115.711 (0.002 115.513 (0.008 115.7003 (0.0006
major A-PAA phase 90 bar, 80 °C minor A-PAA phase 90 bar, 80 °C A phase 150 bar, 40 °C
cPAA is the PAA content in the solid phase.
Table 5. Specific Component of Surface Free Energy of Adsorption, -∆GSP A , Obtained from the IGC Measurements as Function of Process Pressure, Temperature, and Solution Concentration -∆GSP A (kJ/mol) process parameters 90 bar, 80 °C, 0.8 mol % 90 bar, 80 °C, 8 mol % 150 bar, 40 °C, 0.8 mol % 150 bar, 40 °C, 8 mol %
tetradichloro- chloroethyl diethyl hydromethane form acetone acetate ether furan 2.79
1.46
9.47
7.45
5.97
2.47
1.23
6.85
4.58
2.53
3.79
2.07
0.36
8.90
6.66
5.00
6.67
1.45
0.97
7.95
5.71
3.67
5.25
Table 6. Dispersive Component of the Surface Free Energy, γD S , the Acidic, KD, and Basic, KA, Parameters Calculated from the IGC Data as Functions of Process Pressure, Temperature, and Solution Concentration process parameters
90 bar, 80 °C, 0.8 mol %
90 bar, 80 °C, 8 mol %
150 bar, 40 °C, 0.8 mol %
150 bar, 40 °C, 8 mol %
2 γD S (mJ/m ) KA KD
34.4 0.32 0.75
42.0 0.17 0.62
48.4 0.32 0.43
49.7 0.25 0.47
Surface Energetics. The changes of the particle morphology, illustrated by Figure 2, reflect more fundamental changes of the surface structure. The surface energetics can be measured using adsorption of the probe molecules on solid surfaces, in terms of both dispersive and specific components of surface free energy, corresponding to nonpolar and polar properties of the surface. Table 5 shows that the specific component of surface free energy of adsorption, -∆GSP A , for all the polar probes used was the largest for spherical particles produced at 90 bar and 80 °C. However, the ∆GSP A value for samples obtained under the same conditions but with the addition of PAA decreased up to 50%. PAA also decreased -∆GSP A for faceted particles obtained at high pressure. By virtue of their chemical nature, nonpolar probes of the alkane series only exhibit the dispersive component of surface free energy, γD S, which increases with PAA concentration and is larger for the faceted particles obtained at low temperature (Table 6). PAA increased γD S for particles obtained at 90 bar and 80 °C, contrary to the observed decrease of -∆GSP A . For the faceted particles, addition of PAA slightly increased γD S (Table 6). Finally, both the acidity constant, KA, and the basicity constant, KD, decreased with addition of PAA for particles obtained at 90 bar and 80 °C. For samples obtained at 150 bar and 40 °C, addition of PAA decreased KD and increased KA.
Discussion Thermodynamics of A-PAA Solid Solutions. The sensitivity of the entropy of fusion, ∆Sf, of a crystalline substance (the host) to the presence of an impurity or additive (the guest) in solid solution has been quantified in terms of a disruption index (d.i.).26 Specifically, d.i. is given by (b - c) in the following equation:
∆Sf ) ∆Sf° - (b - c) ∆Sidmix
(3)
where ∆Sidmix is the ideal entropy of mixing of the host with the guest, and ∆Sf° is the entropy of fusion of the pure host. In eq 3, b represents the sensitivity of the entropy of fusion of the solid host to the presence of guest, while c represents the sensitivity of the entropy of fusion of the liquid host to the presence of guest. Because crystals are highly ordered, their structure is readily disrupted by the host molecules, whereas liquids are already highly disordered, so the guest molecules have a much smaller effect (i.e., b . c). Hence, d.i. largely reflects the sensitivity of the disorder of the host crystals to the presence of the guest molecules, over and above that associated with the simple dilution effect that is reflected in the ideal entropy of mixing, ∆Sidmix. Although d.i. was originally introduced as an empirical quantity,26 it is directly correlated with the limiting partial molar entropy of the guest in the host crystals, (S2E)0,27 by the following empirical equation:
d.i. ) 0.035[(S2E)0]p, p ) 0.912
(4)
Comparisons of d.i. values have been discussed by Duddu and Grant.28 From the data in Table 2, ∆Sf is plotted against ∆Sidmix in Figure 4b. Although some scatter exists for ∆Sidmix < 0.1 and >0.6 J/K mol, the main part of the plot is linear with the slope between -16 and -23, corresponding to mean (b - c) ) 19. The scatter may be attributed to ethanol present as inclusions in the A crystals at mol fractions of the same order as the mol fractions of PAA in the A crystals. If the mol fraction of ethanol in the A crystals is assumed to be approximately constant, the d.i. value (b - c) of PAA in the A crystals is 19, which corresponds to considerable disruption of the crystal lattice of A by the presence of PAA in solid solution. The d.i. value for PAA and water present together in solid solution in A after crystallization from aqueous solution has been reported as 6.5326 from thermodynamic analysis of the data of Chow et al.29 The moderating effect of the small hydrogen-bonding molecule, water, when present in the A crystals, may explain this smaller value of d.i.
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Table 7. Calculated Mechanical Properties of the Monoclinic (P21/a) Form of A axis/index
a/11
b/22
c/33
stiffness component, c, GPa compliance component, s, GPa-1 Young’s modulus, GPa linear compressibility
15.3 0.12 8.5 0.028
11.5 0.29 3.4 0.071
24.5 0.06 16.5 0.009
From the results in Table 4a on the quantitative analysis of the A phases (A in PAA ) major and PAA in A ) minor), some general conclusions can also be drawn about the elastic strain component, ∆GEl, of the total Gibbs free energy, ∆G. Here, ∆GEl is associated with the elastic strain caused by incorporation of PAA additive, thus
∆GEl = ∆EVmxA-PAA
(5)
∆E ) 0.5cmnmn
(6)
where Vm ) 1.17 × 10-4 m3/mol is the molar volume of A, calculated using the lattice constants in Table 4, xA-PAA is the mol fraction of the minor A-PAA phase, and ∆E is the specific energy of elastic deformation related to the strain matrix, mn. The matrix of elastic constants, cmn, in Table 7 was calculated along the crystallographic axes using the COMPASS force field within the program Cerius2 (Accelrys). The stiffness and compliance components in Table 7 are applicable only if the Cartesian coordinate system used for the elasticity tensor is chosen so that a Cartesian axis coincides with the crystallographic axis under consideration. Therefore, the coordinate system required to obtain the c11 and s11 values for the a axis above is not the same as that required to obtain the c33 and s33 values for the c axis above because the crystal is monoclinic. Young’s modulus and linear compressibility along a given physical direction are independent of the coordinate system. The results obtained here are similar to the theoretical elastic constant results previously obtained23 and also consistent with the experimental Young’s modulus 11.7 GPa previously found.24 Computation using eqs 5 and 6 gives ∆GEl ) 0.80 J/mol ) 5.3 × 10-3 J/g, which is 3-4 orders of magnitude smaller than the characteristic changes of the enthalpy of fusion introduced by addition of PAA (Table 2 and Figure 5). Thus, the contribution of the elastic energy to the total reduction of the Gibbs free energy cannot influence any precipitation or thermodynamic behavior of the A-PAA phases. Surface Structure, Molecular Affinity, and Incorporation Mechanism. At a high temperature, pure A crystals are spherical in contrast to the prismatic, faceted shape at a low temperature and/or high pressure. These morphological changes point to different crystal growth mechanisms that are related to the specific surface free energy, ∆G, of the particles of A. The thermodynamic surface transition observed for A crystals in pure solvent reflects the physical state of the surface. This effect has previously been observed for a number of molecular crystals.25 When the temperature exceeds the roughening transition temperature, TR, the surface growth steps disappear, and the surface becomes rough at a molecular level, which finally results in rounded crystal faces. TR depends on the nature of the material, the molecular structure of a particular crystal face, and the polarity of the solvent and additive. A
Figure 7. Structure of the (110) face of A crystals showing thermodynamic transition from molecularly smooth to molecularly rough surface and strong adsorption sites of PAA molecules (indicated by the arrows) on the molecularly rough surface.
specific feature of the crystal growth of A in supercritical CO2 is that the adsorption and incorporation of PAA molecules in quantities less than 2 mol % increase TR and lead to a significant transformation of the molecular surface. The computer graphic in Figure 7 shows that the {110} faces of A crystals provide the most accessible molecular sites for incorporation of PAA molecules. The acetyl (COCH3) group that distinguishes PAA from A is less disruptive in this case. The IGC results lead to two suggestions. First, the crystal surface of spherical A particles have more exposed OH-proton donor groups and NH-proton acceptor groups on the A molecules than the nonpolar bulky groups (i.e., the benzene ring). Second, the PAA molecule, which is a weaker proton donor than the A molecule, decreases the specific polar interactions and increases the dispersive component of the surface free energy of coprecipitated samples. Therefore, adsorption of PAA into the {110} surface changes the surface free energy: in this case, as the dispersive interactions increase, the polar interactions decrease, and the particle shape changes from spherical to faceted. As a result, the mean volume particle diameter of faceted particles is greater than that of the spherical particles. Adsorption of PAA molecules onto the surface of A particles is followed by incorporation of PAA into the crystal structure producing a solid solution of PAA in A. This process increases the crystal volume free energy, decreases the particle size because
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of depression of the particle growth rate, and increases the surface area of the dominant {110} faces. Conclusion A and PAA form a solid solution during precipitation in supercritical CO2 as a result of their molecular similarity. Incorporation of PAA into the A crystal structure is defined by two major competitive factors, namely, the solubility of PAA at a given pressure and temperature, and the surface molecular structure of the A crystals. The latter also depends on the processing conditions and the PAA concentration. The surface transition is described quantitatively by the dispersive and specific polar interactions derived from IGC data. PAA has a pronounced effect on the precipitation kinetics and modifies the solid-state properties of the resulting A-PAA particles that were characterized in detail using X-ray powder diffractometry and computer modeling. These properties can be predicted on the basis of thermodynamic analysis of solid-solution formation. Acknowledgment. We gratefully acknowledge the continuous support of the SRS Daresbury Laboratory, and in particular, Dr. C. Tang (High Resolution Powder Diffraction). We also thank Dr. J. Osborn (University of Bradford) for kindly providing computation of the elastic constants using the program Cerius (Accelrys, Cambridge, UK). We acknowledge the UK Engineering and Physical Sciences Research Council (EPSRC) for financial support. Some results of this work were presented at the 7th Meeting on Supercritical Fluids, Antibes, 2000. References (1) Fairbrother, J. E. In Analytical Profiles of Drug Substances; Florey, K., Ed.; Academic Press: New York, 1973; Vol. 3, p 1. (2) Chow, A. H.-L.; Grant, D. J. W. Int. J. Pharm. 1988, 41, 29. (3) Shekunov, B. Y.; Grant, D. J. W.; Latham R.; Sherwood, J. N. J. Phys. Chem. 1997, 101, 9107. (4) Debenedetti, P. G.; Tom, J. W.; Yeo, S.-D.; Lim, G.-B. J. Controlled Release 1993, 24, 27.
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