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Sedimentation Field-Flow Fractionation Studies of Ostwald Ripening in Fluorocarbon Emulsions Containing Two Disperse Phase Components Jeffry G. Weers* and Rebecca A. Arlauskas Alliance Pharmaceutical Corporation, 3040 Science Park Road, Sun Diego, California 92121 Received July 29, 1994. I n Final Form: November 16, 1994@ Diffusional mass transfer (Ostwald ripening) between emulsion droplets has been studied. By using sedimentation field-flow fractionation (SdFFF) coupled with gas chromatography, the disperse phase composition can be obtained for monosized droplet fractions. Two liquids, A and B, were mixed together and then emulsified. The mass transfer between droplets of different size was driven by differences in capillary pressure, such that the small particles were enriched in the less soluble B component. At low concentrations of B, a bimodal size distribution emerged, with the small particle size fraction strongly enriched in B. There is a strong agreement between the experimental data and current theories for two-component disperse phase emulsions as developed by Kabalnov et al. (Colloids Surf. 1987,24, 19). different sized droplets, which results from capillary Introduction effects, is balanced by the difference in chemical potential The primary mechanism for coarsening in submicron resulting from partitioning of the two components (similar fluorocarbon emulsions is Ostwald ripening.lI2 Ostwald ripening occurs as a consequence of the Kelvin e f f e ~ t , ~ to Raoult’s law for vaporfliquid equilibria). Higuchi and Misra7derived the followingexpression for the equilibrium which relates that the chemical potential of a disperse condition, wherein the chemical potentials of the medium phase component depends on the curvature of the droplet, soluble component, Ap1, are equal for all of the particles with smaller droplets having a slightly higher local in a polydisperse medium: concentration of the disperse phase adjacent to the drop. Diffusional flow then leads to the growth of the larger ApJRT = (al/aeq) ln(1 - Xeq2)= droplets a t the expense of the smaller ones. The kinetics (al/aeq)- ~,,,(ada,,)~ = constant (2) for the molecular diffusionprocess are most often described in terms of the Lifshitz-Slezov-Wagner (LSW)t h e ~ r y , ~ , ~ which states that, for a single component disperse phase, where Ap1 =p1 - pl* is the excess ofthe chemical potential the cube of the mean number droplet radius, a , increases of the first component with respect to the state p1* when linearly with time at a rate, o: radius a is infinite and XOZ= 0, al= the characteristic length of the medium soluble component = 2uVm1/RT,a0 and aeqare the radii of a n arbitrary particle under initial w = d(aI3/dt = 8oVmCDf(q5)/9RT (1) and equilibrium conditions, respectively, andXozandXeqz are the initial and equilibrium mole fractions of the where u is the interfacial tension a t the oivwater interface, medium insoluble component 2. V,,,is the molar volume of the disperse phase, C and D are The equilibrium determined by eq 2 is stable if the the solubility and diffusion coefficient of the disperse phase derivative of 8Ap&3aeqis greater than zero for all droplets in the continuous phase, f l # ) is a correction coefficient of a polydisperse system. Based on this, the following which takes into account the effect of diffusional interacstability criterion was derived by Kabalnov et a1.8 tions of the droplets a t finite disperse phase volume fractions (#),6 R is the molar gas constant, and T is the X,, > 2a1/3d, (3) absolute temperature. The second result of the LSW theory is that the distribution function of the ratio of the where dois the initial diameter. If the stability criterion initial radius to a critical radius a t any given moment is is met for all droplets, two patterns of growth will result, time-invariant. depending on the solubility characteristics of the secondary To counteract emulsion growth via Ostwald ripening, component. If the secondary component has zero solubility Higuchi and Misra7 proposed the addition of a second in the continuous phase, then the size distribution should disperse phase component which is insoluble in the not deviate significantly from the initial one, and the continuous phase. In this case, significant partitioning growth rate should be equal to zero. In the case of limited of the two disperse phase components between different solubility of the secondary component, the distribution is sized droplets is predicted, with the component having governed by rules similar to the LSW theory (i.e. the low water solubility being expected t o be concentrated in distribution function is time-invariant), and the growth the smaller droplets. During Ostwald ripening in tworate should be given by: component disperse phase systems, equilibrium is established when the difference in chemical potential between (4)
+
@
Abstract published in Advance A C S Abstracts, February 1,
1995. (1)Ostwald, W. 2. Phys. Chem. (Leipzig)
1900,34, 295. ( 2 )Kabalnov, A. S.; Shchukin, E. D. Adu. Colloid Interface Sci. 1992, 38, 69. (3) Thomson, W.(Lord Kevin) Proc. Royal SOC.,Edinburgh 1871,7, 63. (4) Lifshitz, I. M.; Slezov, V. V. Sou. Phys. JETP 1959,35,331. (5) Wagner, C.2. Electrochem. 1961,35,581. (6) Braisford, A. D.; Wynblatt, P. Acta Metall. 1979,27,489. (7) Higuchi, W. I.; Misra, J. J . Pharm. Sci. 1962,51, 459.
0743-7463/95/2411-0474$09.00/0
If the stability criterion is not met, a bimodal size distribution is predicted to emerge from the initially unimodal one. Since the chemical potential of the soluble component is predicted to be constant for all droplets, it is also possible to derive the following equation for the quasi-equilibrium (8) Kabalnov, A. S.; Pertsov, A. V.; Shchukin, E. D. Colloids Surf. 1987,24,19.
0 1995 American Chemical Society
SdFFF Studies of Ostwald Ripening
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The goal of this paper is to experimentally test these theoretical predictions. Field-flow fractionation (FFF) is a series of elution methods which are analogous to liquid chromatography and can be used to fractionate a broad range of samples from molecules as small as 100 Da up to droplets as large as ca. 100 , ~ m FFF . ~ consists of several subtechniques which differ in the type of applied field. The various subtechniques which include sedimentation, thermal, crossflow, or electrical are responsive to different particle properties and are applicable to different parts of the overall size range. Sedimentation field-flowfractionation (SdFFF)is used in this study because the measured elution volume of the sample is directly related to the effective mass of the constituent particles by well-established equations, provided the densities of both the particles and the suspension medium are known. In SdFFF, separation develops along the flow axis a t right angles to the driving force. It is possible, therefore, to generate monosized fractions of particles across the droplet size distribution. SdFFF utilizes a n applied external centrifugal field to order droplets according to their size, with the larger slower diffusing droplets accumulating near the wall of a ribbon-like channel. The ordered array is then subjected to a laminar flow of a mobile phase so that the particles near the wall move slowly compared to those in midstream. This combination of field and flow leads to enhanced separation, with the smaller droplets exiting first. In the current study, SdFFF allows us to directly measure the mass transfer process that occurs in twocomponent fluorocarbon emulsions. By collecting monosized fractions across the droplet size distribution and analyzing for fluorocarboncontent by gas chromatography, it is possible to experimentally ascertain the partitioning of fluorocarbon components which has been up until now only theorized to occur between different sized droplets. Materials and Methods Materials. Periluorooctylbromide (PFOB)and perfluorodecyl
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Figure 1. Linear plots of a3 vs time found for 90% w/v PFOB/ PFDB emulsions ( ~ P F D B= 0, 0.01, 0.1) stabilized by 4% w/v EYP. The storage temperature is 40 "C. The inset shows the changes in growth rate found as a function of added PFDB. The curve represents the fit to eq 4. the wavelength, the signal depends on both mass in the detector and on particle diameter to a high power. The Gafford scattering correction, which takes into account the particle size dependence on the optical density, has been applied to the photosedimentation data.12 Droplet size distributions and disperse phase partitioning was determined by SdFFF (model S101, FFFractionation Inc., Salt Lake City, UT). The instrumental conditionshave been described previ0us1y.l~The fractograms contain no scattering correction, hence they slightly overestimate the value of the median diameters. For the droplet partitioningstudies, a 100pLinjection of the polydisperse emulsion sample was fractioned using the SdFFF and monosized fractions of fluorocarbon droplets were collected across the distribution of droplet sizes. The fractions were extracted into isooctane using a procedure which has been shown to be precise (coefficientof variation of less than 8%)and accurate (readback recoveries ranging from 86 to 110%). The fractions were then analyzed by gas chromatography (electron capture detection) for fluorocarbon content. All fluorocarbons were quantitated using external standards and a linear regression equation that accurately characterized the calibration curve (linear range from 0.5 to 1000 pglmL). Gas chromatographic measurements were made on a model 5890 Series I1 instrument obtained from Hewlett-Packard (Santa Clara, CA).
bromide (PFDB) were obtained from Atochem (Paris, France). Their purities were 99.9 and 98.9% respectively. Egg yolk phospholipid (EYP) was obtained from Kabi Pharmacia (Stockholm,Sweden). All materials were used as received. Methods. Concentrated emulsions containing 90%w/v total fluorocarbon (47% v/v), 4% wlv EYP, and the usual complement of physiological salts, buffers, and antioxidantslo were manufactured on a model M-110 microfluidizer (Microfluidics,Newton, MA). Incipients included 0.24% wlv NaCl, 0.355% w/v NazHPO4-7H20,0.052%w/vNaH2P04.H20,0.02% w/v CaNa2EDTA, and 0.002% wlv a-tocopherol. Emulsions were processed at 12 000 psi for five discrete passes (2' = 45 "C) and terminally sterilized a t 121 "C in a rotating autoclave under conditions described previously.ll The emulsions were subsequently stored a t 40 "C for accelerated stability testing. For the kinetics studies the droplet size was determined via photosedimentation (modelCAPA-700,Horiba Instruments Inc., Irvine, CA). In photosedimentation, a centrifugal field is applied to a dilute emulsion sample, and the particle size is determined from changes in the optical density. Optical detection of the particles is complicated because the relationship between the optical density and the mass of particles being detected depends strongly on particle size. Specifically, particles which are much larger than the detector wavelength are good scatterers, and their signal is simply related t o mass concentration in the detector and is independent of diameter. For particles much smaller than
Results Kinetics of Emulsion Growth in PFOBPFDB Mixtures. Figure 1is a plot ofa3vs time for concentrated (90% w/v total fluorocarbon) emulsions containing two disperse phase components. The primary fluorocarbon in this study is PFOB, while the minor (low water solubility) component is PFDB. All of the emulsions are stabilized by 4% w/v EYP. The linear plots of a3vs time are in agreement with LSW theory (eq 11, providing evidence that Ostwald ripening is the primary mechanism of irreversible droplet growth in these emulsions. The o value obtained for PFOB (2.1 x lowz7m3/s) is in good agreement with the value of 2.7 x m3/s obtained by Kabalnov et al.14 Addition of as little as 1%w/w PFDB to the PFOB emulsion (volume fraction of PFDB = ~ P F D Bx 0.01) decreases the growth rate by greater than 3 times. Addition of 10%w/w PFDB ( ~ P F D Bx 0.1) leads to a n order of magnitude decrease in the particle growth rate. The increases in PFOB emulsion stability afforded by the addition of the less soluble PFDB component are in agreement with the predictions of Higuchi and Misra.' The inset in Figure 1 is a plot of the mixture growth rate, wmix, vs @ ~ F D B . The curve through the points represents the fit to eq 4.
(9) Giddings, J. C. Science 1993,260, 1456. (10) Riess, J. G.; Dalfors, J. L.; Hanna, G. K.; Klein, D. H.; Krafft, M.-P.; Pelura, T. J.; Schutt, E. G. Biomat. Art. Cells Immob. Biotech. 1992,20,839. (11)Dalfors, J.; Espinosa, C. A. Biomat. Art. Cells Immob. Biotech. 1992,20,853.
(12) Gafford, R. D. Polym. Mater. Sci. Eng. 1985,53,358. (13)Arlauskas, R. A.; Burtner, D. R.; Klein, D. H. In Chromatography ofPolymers;Provder, T., Ed.; ACS Symp. Ser., 521,AmericanChemical Society: Washington, DC, 1993; pp 1-12. (14) Kabalnov, A. S.;Makarov, K. N.; Shchukin, E. D. Colloids Surf. 1992,62, 101.
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Figure 2. Typical SdFFF fractogram obtained for a 90% w/v PFOBPFDB emulsion( ~ P F D B= 0.1) after 1month at 40 "C. The shoulder which appears adjacent to the void volume peak is due to phospholipid vesicles, while the peak at around 0.2 pm is due to fluorocarbon emulsion droplets stabilized by a monolayer of phospholipid.
Figure 4. Changesin the component partitioning as a function ofterminalsterilizationand storage observed for 90%w/v PFOB/ PFDB emulsions ( ~ P F D B= 0.1). The storage temperature is 40 "C.
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Figure 3. SdFFF study illustrating the partitioning which occurs as a function of droplet size in 90% w/v PFOBPFDB emulsions ( + ~ F D B = 0.1) stabilized by 4% w/v EYP. The fractogram (left axis) was measured immediately after manufacture (prior to terminal sterilization). The right axis (given by triangles in the plot) represents the XPFDB in various monosized droplet fractions as determined by gas chromatography. PFOB and PFDB are found to be enriched in the large and small drops, respectively.
SdFFF Studies in Emulsions Containing T w o Disperse Phase Components. Figure 2 presents a typical SdFFF fractogram obtained for a PFOBPFDB emulsion ( ~ P F D B= 0.1) stabilized by 4%w/v EYP after 1 month of storage a t 40 "C. The data are presented as a mass weighted detector response vs droplet diameter. The shoulder which appears next to the sharp initial void volume peak is due to the presence of phospholipid vesicles which contain only small amounts of solubilized fluorocarbon.13 The larger sized (latereluting) peak is attributed to fluorocarbon emulsion droplets which are stabilized by an interfacially adsorbed monolayer of phospholipid. Figure 3 illustrates the partitioning of disperse phase components that occurs between various monosized droplet fractions in a PFOBPFDB emulsion ( ~ P F D B= 0.1) immediately after manufacture and before sterilization (presterile). Shown in Figure 3 are the SdFFF fractogram (plotted on the left axis)and mole fraction of PFDB (XPFDB) in different monosized droplets as obtained by gas chromatography (bulk XPFDB = 0.085). The bulk composiexpected across the entire particle size tion is the XPFDB distribution in a coalescence mediated process, since no partitioning of components between droplets can occur by this mechanism. The reported points (fSD)are the results obtained for three independently manufactured formulations. It is clear that the smaller droplets are significantly enriched in the slower diffusing PFDB component (by 10%
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Figure 5. SdFFF fractogram obtained for a 90% w/v PFOB/ PFDB emulsion ( @ ~ F D B = 0.03), stabilized by 4% w/v EYP, illustrating a bimodal distribution of droplets.
or more), while the larger droplets are enriched by up to 20%in PFOB. Figure 4 illustrates the changes in the droplet partitioning following terminal sterilization and storage a t 40 "C. After 1 month, the sample has evolved such that the smaller droplets (i.e. those less than the median diameter of 0.23 pm) have a n XPFDB x 0.105. These droplets are enriched by ~ 2 4 % in PFDB over bulk compositions. On the other hand, larger droplets (e.g. 0.36 pm) have an XPFDB = 0.07, i.e. enriched by 18%in the more soluble, faster diffusing PFOB component. After 4 months the larger droplets are enriched in PFOB to an even greater ) a t 1 month. The smaller droplets extent ( ~ 2 9 %than have now shrunk to the extent that significant fractions are eluted in the void volume. TheXPFDBin the void volume ( ~ 0 . 1 4suggests ) that these droplets are enriched in PFDB by 65%over the expected bulk compositions. This data provides the first experimental proof of component partitioning in two-component disperse phase emulsions, which had previously only been predicted t h e ~ r e t i c a l l y . ~ , ~ The degree of component partitioning between different sized droplets is expected to be greater when only small amounts of secondary fluorocarbon are added. Figure 5 shows a n SdFFF fractogram, obtained immediately after sterilization, for a PFOBPFDB emulsion ( ~ P F D Bx 0.03) stabilized by 4%wlv EYP. The separation of a distinct distribution of small droplets enriched in the PFDB component having low water solubility is observed (Le. a bimodal distribution of emulsion droplets). Figure 6 is a plot of XPFDB VS lld for the the ~ P F D B= 0.1 sample prior to sterilization, where lld is obtained from the SdFFF data in Figure 4. The slope of a plot of XPFDB VS lld should be equal to 2 Q p ~ (eq o ~ 5). ~ Q P F O BiS equal
Langmuir, Vol. 11, No. 2, 1995 477
SdFFF Studies of Ostwald Ripening 0.12 I 0.11
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Figure 6. Plot of X ~ F (obtained ~B by gas chromatography) vs l/d for a 90%w/v PFOBPFDB emulsion ( ~ F D = B 0.1) stabilized by 4% w/v EYP. The emulsion was analyzed immediately after manufacture and was not terminally sterilized. The slope of the lines is predicted to be equal t o twice the characteristic length, UPFOB. The agreement between theory and experiment is excellent.
to 0.0017, so the agreement between theory and experiment is excellent.
Discussion Higuchi and Misra7 predict that the addition of a secondary disperse phase component that has little solubility in the continuous phase will stabilize emulsions with respect to Ostwald ripening. Further, they predict that significant partitioning of the two components between different sized droplets will occur. The enhanced stability of PFOB emulsions afforded by the addition of PFDB (Figure 1 ) is in excellent agreement with their predictions. As well, the component partitioning observed with the less soluble PFDB component being enriched in the small droplet fraction and the more soluble PFOB being enriched in the large droplet fraction (Figures 3 and 4) are in good qualitative agreement with their theory. The theory of Kabalnov et a1.8predicts that two patterns of growth will occur in emulsions for which the stability parameter (given by eq 3) has been met. Ifthe stabilizing component has no solubility in the continuous phase, then no growth is expected. If the secondary component has a small but finite solubility, then the growth is expected to obey eqs 4 and 5. The stability parameter for PFOBI PFDB emulsions depends critically on XPFDB and u. The measurement of u for long chain phospholipids is problematic for two reasons: the solubility in both fluorocarbon and water is poor, and the diffusion of phospholipid to the fluorocarbodwater interface is extremely slow. Recent studies by Burgess andYoon15report a value of ca. 50 mN/m for long chain phospholipids a t bis(F-buty1)ethenelwater interfaces (7 x g/L phospholipid). This value cannot be considered to be a n equilibrium value, however, and reflects only the extremely slow kinetics for adsorption of phospholipid to the interface, which can be on the order of years for EYP. It is not likely, therefore, that any technique can accurately measure the equilibrium interfacial tension of long chain phospholipids. Recent studies by Kabalnov in which the interfacial tension for long chain phospholipids a t PFOBl water interfaces is extrapolated from accurate studies of the more water soluble short chain phospholipid analogues estimates u to be approximately 4 mN/m for EYP.l6 Using this value of u, the stability criterion is predicted to hold for all droplets whose diameter is greater than 0.02 pm ( ~ P F D B = 0.03) and 0.007 pm ( ~ ~ F D= B 0.1). Thus, the (15)Burgess, D.; Yoon, J. K. Colloids Surf. B 1993, 1 , 283. (16) Kabalnov, A. S., personal communication.
stability criterion is expected to hold for virtually all of the droplets in either emulsion formulation. It would be predicted, therefore, that the increases in stability afforded by addition of PFDB to PFOB emulsions as shown in Figure 1 should be predicted by eq 4. Indeed, the agreement between the points and theory of the inset of Figure 1 are excellent. It is interesting that a distinctly bimodal distribution of droplets is observed for the emulsion containing small quantities of added PFDB ( ~ P F D B= 0.03). This reflects the large degree of partitioning expected when the volume fraction of stabilizing fluorocarbon is low. The fact that a distinctly bimodal distribution emerges may suggest that the stability criterion may in fact not hold for these low concentrations of added PFDB. Another condition which should be obeyed, provided that the stability criterion is met for all droplets is given by eq 5, predicts that the slope of plots ofXz vs lld should be equal to 2al. Plots of XPFDB vs lld for the presterile ( ~ F D B 0.1) sample shown in Figure 6 are in excellent agreement with the theory (assuming u = 4 mN/m for EYP a t the PFOBlsaline interface). The same cannot be said for the samples which were terminally sterilized, however. In this case the slopes deviate significantly from 2al. As well, plots OfXPFDB vs diameter (Figure 4)show a curious leveling off at small diameters. This observation is inconsistent with current theories which predict that the partitioning should continue to increase. During terminal sterilization, emulsion samples are heated to 121 "C for a n extended period of time. During this process, the droplet size increases significantly (by 50% or more). The droplet coarsening during this procedure probably involves significant coalescence. Thus, although the poststerile samples agree qualitatively with theory (i.e. droplet partitioning is observed), they do not agree quantitatively, and this lack of agreement is probably related to significant coalescence during terminal sterilization. It is interesting to note that significant partitioning of the disperse phase components occurs during processing. This result reflects that there is sufficient processing energy to make much smaller droplets, but Ostwald ripening quickly coarsens the small droplets to a larger size. Thus, Ostwald ripening is also the primary determinant of initial droplet size in these emulsion^.'^
Summary Direct experimental evidenceis provided for partitioning of disperse phase components in different sized droplets of a two-componentdisperse phase emulsion. Specifically, this study provides the first experimental evidence that molecular diffusion in two-component mixtures leads to an increase in the mole fraction of the less soluble component in the smaller droplets. Evidence is also provided for the development of bimodal distributions at low volume fractions of the stabilizing component. The partitioning data is in excellent agreement with current theories for two-component disperse phases provided that the sample is not terminally sterilized. It is hypothesized that terminal sterilization leads to significant emulsion coalescence, thereby leading to the deviations from theory observed. Acknowledgment. The authors wish to thank Alexey Kabalnov, Leo Trevino, David Klein, and Eric Kaler for helpful discussions. LA940600+ (17) Weers, J. G.; Ni, Y.; Tarara, T. E.; Pelura, T. J.;Arlauskas, R. A. Colloids Surf. A 1994, 84,81.
