Langmuir 1997, 13, 3047-3051
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Swelling of Polystyrene Latex Particles in Water by High-Pressure Carbon Dioxide Katsuto Otake,† Stephen E. Webber,‡ Petr Munk,‡ and Keith P. Johnston*,† Departments of Chemical Engineering and Chemistry, University of Texas, Austin, Texas 78712 Received September 3, 1996. In Final Form: March 14, 1997X The swelling of a 50 nm monodisperse polystyrene latex by carbon dioxide was measured by dynamic light scattering at 25 °C at pressures up to 35 MPa. At the higher pressures, the polystyrene (PS) latex swelled by up to 1.6 times as much as bulk PS. This enhanced swelling is due largely to the adsorption of CO2 into the interfacial region, which lowers the overall interfacial tension between the latex and water phases. On the basis of this enhanced swelling, the thickness of the interfacial region containing PS, carbon dioxide, and water is approximately 4 nm, which is on the order of the radius of gyration of a PS chain.
Introduction Polymer latex particles suspended in water are of interest in many practical applications including immunoassay and drug delivery systems. A hydrophobic drug may be impregnated into a latex particle by equilibration between the aqueous phase and the latex particle phase. The diffusion of the hydrophobic drug into the latex particles, which are often in a glassy state, can be unacceptably slow. If the solubility of the drug is low in water, the small driving force for diffusion into the particles can contribute even further to the slow kinetics. The diffusion rate could be increased significantly by plasticizing the latex particles, for example with a supercritical fluid. In recent years, supercritical fluid CO2 has received significant attention as an environmentally benign alternative to organic solvents.1-7 Supercritical fluids, especially CO2, are often smaller than liquid solvents and can diffuse quickly into glassy polymers to produce a significant degree of swelling and plasticization.8-17 The * To whom correspondence should be addressed. † Department of Chemical Engineering. ‡ Department of Chemistry. X Abstract published in Advance ACS Abstracts, May 1, 1997. (1) Shim, J. J.; Johnston, K. P. AIChE J. 1989, 35, 1097-1106. (2) DeSimone, J. M.; Guan, Z.; Elsbernd, C. S. Science 1992, 257, 945. (3) Goel, S. K.; Beckman, E. J. Polym. Mater. Sci. Eng. 1992, 67, 506. (4) Hutchenson, K. W.; Foster, N. R. Innovations in Supercritical Fluids; American Chemical Society: Washington, DC, 1995; Vol. 608. (5) Savage, P. E.; Gopalan, S.; Mizan, T. I.; Martino, C. J.; Brock, E. E. AIChE J. 1995, 41, 1723. (6) Johnston, K. P.; Harrison, K. L.; Clarke, M. J.; Howdle, S. M.; Heitz, M. P.; Bright, F. V.; Carlier, C.; Randolph, T. W. Science 1996, 271, 624. (7) Johnston, K. P.; Lemert, R. M. In Encyclopedia of Chemical Processing and Design; McKetta, J. J., Ed.; Marcel Dekker: New York, 1996; Vol. 56; pp 1-45. (8) Wissinger, R. G.; Paulaitis, M. E. J. Polym. Sci., Part B: Polym. Phys. 1991, 29, 631. (9) Wissinger, R. G. Dissertation Thesis, University of Delaware, 1994. (10) Condo, P. D.; Johnston, K. P. Macromolecules 1992, 25, 6730. (11) Condo, P. D.; Sanchez, I. C.; Panayiotou, C. G.; Johnston, K. P. Macromolecules 1992, 25, 6119. (12) Condo, P. D.; Paul, D. R.; Johnston, K. P. Macromolecules 1994, 27, 365. (13) Condo, P. D.; Johnston, K. P. J. Polym. Sci.: Part B: Polym. Phys. 1994, 32, 523. (14) Kamiya, Y.; Mizoguchi, K.; Naito, Y. J. Polym. Sci., Polym. Phys. Ed. 1990, 28, 1955. (15) Sada, E.; Kumazawa, H.; Yakushiji, H.; Bamba, Y.; Wang, S.-T. Ind. Eng. Chem. Res. 1987, 26, 433. (16) Handa, Y. P.; Lampron, S.; O’Neill, M. L. J. Polym. Sci. Polym. Phys. Ed. 1994, 32, 2459.
S0743-7463(96)00855-4 CCC: $14.00
glass transition is depressed in proportion to the solubility of the fluid in the polymer, as predicted theoretically with lattice-fluid theory and the Gibbs-Di Marzio criterion.11 Depressions of over 50 °C are common. The ability to control the swelling and Tg with pressure offers interesting opportunities for polymer processing. For example, polymers can be purified by the removal of monomers, oligomers, and undesired solvent or impregnated with a variety of additives.1,18-20 After being processed, the CO2 diffuses out of the polymer rapidly upon depressurization, without leaving solvent residues. To date these approaches have been applied to bulk polymers but not to polymer latexes in water. Our objective was to measure the swelling of 50 nm polystyrene latex spheres in water saturated with CO2, by dynamic light scattering. Three phases were equilibrated, a liquid or vapor CO2 phase containing small amounts of dissolved water, an aqueous phase containing small amounts of dissolved CO2, and the latex spheres suspended in the aqueous phase. The pressure was varied from 0 to 35 MPa. The results are compared with swelling data for bulk polystyrene (PS) equilibrated with CO2. The differences between the swelling of bulk PS and the PS latex particles are analyzed in terms of the effect of the PS-water interfacial tension on the solvent activity, the incorporation of water into the latex particles, pH, and the adsorption of CO2 into the interfacial region of the latex particles. Experimental Section Materials and Apparatus. Monodisperse, low surface charge, and surfactant-free polystyrene (PS) latex was purchased from Polyscience, Inc. (Polybead Microparticle, 0.05µm) as a 2.5 wt % aqueous solution. The latex spheres were not cross-linked. Experiments were performed with a sample which was diluted to a concentration of 0.065% by weight. The latex was stabilized by electrostatic repulsion between dissociated sulfonic acid groups on the PS. Filtered, degassed, and deionized water was used as a diluent. CO2 was obtained from Linde (Bone Dry Grade, 99.8%). The sample solution was filtered with a 0.45 µm membrane filter and loaded into the scattering cell (Figure 1), which contained three sapphire windows at right angles. The scattering angle was 90°. The hydrodynamic diameter of the latex particles was (17) O’Neill, M. Dissertation, Carleton University 1994. (18) Berens, A. R.; Huvard, G. S. In Superctitical Fluid Science and Technology; Johnston, K. P., Penninger, J. M. L., Eds.; American Chemical Society: Washington, DC, 1989; Vol. 406; pp 207-223. (19) Sayegh, S. G.; Najman, J. Can. J. Chem. Eng. 1987, 65, 314. (20) Condo, P. D.; Sumpter, S. R.; Lee, M. L.; Johnston, K. P. Ind. Eng. Chem. Res. 1996, 35, 1115-1123.
© 1997 American Chemical Society
3048 Langmuir, Vol. 13, No. 11, 1997
Otake et al. τ is fitted to a second-order polynomial. The coefficient of the first-order term is an average decay rate, q2D h , where D h is the average diffusion coefficient. Equation 4 is used to calculate an average droplet size from D h . The coefficient of the second-order term is defined as a polydispersity index, which goes to zero for a monodisperse solution. A highly monodisperse latex typically has a polydispersity index from 0 to 0.02. In the present study, it ranged from 0.005 to 0.05, indicating that the presence of CO2 did not disturb the quality of the optical measurements. We assumed that the viscosity of the water saturated with CO2 is the same as that of pure water19 and obtained the viscosity of water at each temperature from the literature.21 The refractive index of pure water was used for the continuous phase, since the solubility of CO2 in water is small, and the refractive index for liquid CO2 (1.20 at 112 MPa and 25°C) is not that far from that of water (1.35 at 25 °C). The saturated CO2 in water changes the refractive index by less than 1%.
Results and Discussion
Figure 1. Schematic of the high-pressure light scattering cell. measured with a dynamic light scattering apparatus equipped with a digital correlator with 72 real time channels (Brookhaven Instruments Corp. Model BI-2030AT). The sample time was 15 µs per channel, and the total duration for each size measurement was approximately 2 min. The incident beam was from a heliumneon laser (λ ) 632.8 nm) mounted to a Brookhaven Model BI200 goniometer. A Lauda Model RMS-6 recirculator provided temperature control of the scattering cell. The dynamic light scattering measurements were performed at 25 °C as a function of pressure. The latex solution was equilibrated for 30 min at each pressure. During equilibration, the solution was stirred with a magnetic stir bar inside the scattering cell. Without stirring, several hours were required to achieve swelling equilibrium. On the other hand, with stirring, equilibrium was obtained within 20 min. The uncertainties of the temperature and pressure were less than +0.1 °C and +0.01 MPa, respectively. Particle Diameter. The intensity autocorrelation function is given by
G2(τ) ) 〈I(τ) I(t + τ)〉
(1)
where I(t) is the intensity of scattered light at a given time and τ is a delay time. Provided that the number of particles in the scattering volume is large enough, the intensity autocorrelation function is related to the modulus of the field autocorrelation function g1(τ) by
G2(τ) ) A + B[g1(τ)]2
(2)
where A and B are instrumental factors. For a solution of monodisperse spherical particles, g1(τ) is given by
g1(τ) ) exp(-q2Dτ)
(3)
where q ) (4πn/λ0) sin(θ/2), n is the refractive index of the continuous phase, λ0 is the wavelength of the incident light, θ is the scattering angle, q is the scattering vector, and D is the diffusion coefficient of the droplets in solution. From the diffusion coefficient, the hydrodynamic diameter can then be calculated using the Stokes-Einstein equation
d ) kBT/3πηD
(4)
where kB is Boltzmann’s constant, T is the temperature, and η is the viscosity of the continuous phase. For a solution of polydisperse spherical particles, eq 3 becomes a multiexponential function. The cumulants method was employed to obtain an average droplet size and polydispersity index from g1(τ).35 In this method, the natural log of g1(τ) versus
The ratio of the hydrodynamic diameter of the swollen latex particle to the diameter at the same temperature before CO2 was added was measured as a function of pressure. Within the experimental time scale of 12 h, there was no sign of flocculation, and after the release of pressure, the particle diameter returned rapidly to its original value. The low polydispersity index reported above is strong evidence that flocculation was not present. However, the latex flocculated when pressurized for over 36 h, and the particle size would not return to the original value after depressurization. The hydrodynamic diameter versus pressure isotherms exhibited complex behavior, as is often the case when pressure is chosen as the independent variable. Pressure is not a very useful indicator of the solvent characteristics of carbon dioxide, as small changes in pressure can cause large changes in solvent density. The solvent density and solvent activity are much more informative thermodynamic variables.1 The activity is defined as f/f sat where f is the fugacity of CO2 at a given temperature and pressure and f sat is the fugacity at the same temperature and saturation pressure. The activity representation of the data is much simpler than the pressure representation, as the logarithm of the activity is related directly to the chemical potential. Both f and f sat were determined from an accurate equation of state.22 For temperatures above the critical temperature, f sat , is determined by extrapolation of the vapor pressure curve. To illustrate the usefulness of the activity as a thermodynamic variable, the solubility of CO2 in bulk PS is shown as a function of the activity of CO2 in Figure 2. Over this range the isotherms from four different laboratories essentially collapse onto a universal curve over a wide range in temperature. The dot-dash line is a leastsquares fit of all of the data. A much greater variation with temperature is observed for the same plot as a function of pressure. In Figure 3, the ratio of the volume of the PS latex to that at ambient pressure, V/V0, is shown as a function of the activity of pure CO2. This ratio is simply the cube of the ratio of the hydrodynamic diameters. In addition, the sorption of CO2 in bulk PS from Figure 2 is plotted. The CO2 induced swelling of the PS latex in water is much larger than the swelling of bulk PS (without water present). The latex was not cross-linked. If it were, the swelling would have been lower. (21) Steam Tables; Eng., J. S. M., Ed.; Japan Society of Mechanical Engineers: Tokyo, 1980. (22) Ely, J. F. CO2PAC: A Computer Program to Calculate Physical Properties of Pure CO2; National Institute of Standards and Technology: Washington, DC, 1986.
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developed a simple theory for the swelling of a latex particle by a water immiscible solvent, based in part upon FloryHuggins theory. In the extension of this theory by Gardon,24 the free energy change of the latex particle due to isotropic swelling is represented by the sum of two contributions, the free energy of mixing and the interfacial free energy. The resulting expression for the activity of the solvent a1 is
ln a1 ) ln(1 - Φ2) + Φ2 + χΦ22 + (2vj 1γ/r0RT)Φ21/3 (5)
Figure 2. Solubility of CO2 in bulk polystyrene (PS) as a function of CO2 activity (closed symbols, ref 38; open symbols, ref 17; lines, ref 15).
where Φ2 is the volume fraction of polymer in the particle, χ is the polymer-solvent interaction parameter, vj 1 is the partial molar volume of solvent in the latex, chosen as the van der Waals volume for CO2, 42.7 cm3/mol, γ is the latexwater interfacial tension, and r0 is the unswollen radius of the solvent-free particle. The theory was extended further by Bindschaedler et al.25 who considered the incorporation of water into the latex particle with solvent and regarded the system as a three-component system. The equation of Morton et al. is a specific case of this theory where water does not penetrate the latex particle beyond the surface. The theory of Morton et al. may be used to gauge the effect of the styrene-water interfacial tension. The CO2 equilibrates between the gas phase, the aqueous phase, and the PS latex phase. The condition of equilibrium for CO2 between the vapor (V) and polymer (P) phases is given by1,26
f1V ) f1P ) a1f1sat exp[vj 1(P - Psat)/RT]
(6)
Taking the logarithm of both sides of eq 6 and substitution of eq 5 for ln a1 yields
ln(1 - Φ2) + Φ2 + χΦ22 + (2vj 1γ/r0RT)Φ21/3 ) ln(f1V/f1sat) - vj 1(P - Psat)/RT (7)
Figure 3. Swelling of PS latex particles with the addition of CO2 at 25 °C for pressures from 0 to 35 MPa. The swelling is determined from the hydrodynamic radii: V/V0 ) (d/d0)3. For comparision, the swelling of bulk PS without water present from Figure 2 is shown.
For sorption studies of CO2 in bulk PS, the pressure could not be increased above 10 MPa. Above this pressure, the marked swelling caused the PS sample to lose its shape and physical integrity, and the length change could no longer be measured. This limitation is not present for the latex particles, which were studied up to 35 MPa. Several factors may be considered to explain the greater swelling of the PS latex versus bulk PS: (1) the effect of the PS-water interfacial tension on the solvent activity; (2) the incorporation of water into the latex particles which could influence the uptake of CO2; (3) the change in pH with dissociation of carbonic acid which could influence the surface charge density; (4) adsorption of CO2 at the water-latex interface. The second factor is unlikely since PS is highly hydrophobic, and the solubilities of water into PS- and CO2-rich domains within PS are low. For example, the solubility of water in CO2 is only 0.3 wt % at 30 °C and 30 MPa. It is easy to show that the first factor above is unimportant at the conditions studied. Morton et al.23
The gas phase was treated as pure CO2, as the presence of less than 1 wt % of dissolved water will have little effect on the fugacity of CO2. To analyze the latex swelling data with eq 7, χ was determined by correlating swelling data for bulk PS up to an activity of unity (see Figure 2). The value of χ varied from 1.6 to 2 over this activity range. The interfacial tension between styrene and water, γSW, can be approximated by that between water and toluene, which is 35 dyn/cm.27 On the basis of the PS-water and waterair interfacial tensions, the interfacial tension between PS and water is about 30% larger than this, which will not affect the results given below. This theory predicts a negligible change in swelling due to the interfacial term. Because swelling increases the interfacial area, this theory predicts that the swelling of the latex would be less than that of the bulk, which is the opposite of the experimental results. Clearly, the interfacial tension between PS and water is not what enhances the swelling of the latex compared with the bulk PS. The dissociation of the dissolved CO2 in water lowers the pH significantly and has the potential to change the surface charge density on the latex particles. To calculate (23) Morton, M.; Kaizerman, S.; Altier, M. W. J. Colloid Sci. 1954, 9, 300. (24) Gardon, J. L. J. Polym. Sci. 1968, 6, 2859. (25) Bindschaedler, C.; Gurny, R.; Doelker, E.; Peppas, N. A. J. Colloid Interface Sci. 1985, 108, 75. (26) Prausnitz, J. M.; Lichtenthaler, R. N.; Azevedo, E. G. d. Molecular Thermodynamics of Fluid-Phase Equilibria, 2nd ed.; Prentice-Hall: Englewood Cliffs, NJ, 1986. (27) Adamson, A. W. Physical Chemistry of Surfaces, 5th ed.; Wiley: New York, 1990.
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Otake et al.
Figure 4. Calculated pH of water saturated with CO2.
the pressure dependence of the pH for water saturated with CO2, it is necessary to determine: (1) the solubility of CO2 in water28-30 and (2) the pressure dependence of the dissociation constant of CO2. The solubility of CO2 into water S (g of CO2/g of H2O) was correlated with the following expression
S ) ax-1/2 + bx + cx2
(8)
where x is the activity of CO2 in the gas phase, f/fsat. The correlated parameters are a ) -1.3481 × 10-3, b ) 0.0764, and c ) -0.0195. The pressure dependence of the dissociation of carbonic acid in water was estimated by the equation proposed by North.31 At high pressure, the pH is approximately 3, whereas the pKa is 2 for the dissociation of the sulfonic acid group on the latex (Figure 4). Since the sulfonic acid groups will not be reprotonated to a significant extent, flocculation of the latex particles due to loss of surface charge may be expected to be small over several hours. This expected result was observed experimentally, as the measured changes in particle diameter of the latex and the polydispersity did not indicate any significant flocculation over 12 h. We now consider the fourth possibility, the surface adsorption of CO2. The surface excess of carbon dioxide at the PS-water interface is described by the Gibbs adsorption equation. A surface excess of carbon dioxide will be present at this interface if carbon dioxide lowers the interfacial tension. This surface excess is expected since the interfacial tension between CO2 and water, γCW, and that between CO2 and PS are far less than γ between PS and water. Consequently, CO2 will adsorb at the latex interface to lower the overall interfacial tension. The interfacial tension between styrene and water, γSW, is on the order of 35 dyn/cm, as mentioned above. The interfacial tension between CO2 and water, , changes with CO2 pressure as shown in Figure 5. It falls between 20 and 30 dyn/cm over most of the range studied in the PS latex swelling experiments. The cohesive energy density of CO2 is always less than that of water. As the pressure increases, the density and activity of CO2 increase, raising its cohesive energy density. The change in the cohesive energy density of water with pressure is very small. As the difference between the water and CO2 cohesive energy densities decreases, γCW decreases as expected, except near the critical point.32 The large dip in γCW near the critical point of CO2, 31 °C and 7.4 MPa, is due to the large Gibbs (28) Wiebe, R.; Gaddy, V. L. J. Am. Chem. Soc. 1939, 61, 315. (29) Wiebe, R.; Gaddy, V. L. J. Am. Chem. Soc. 1940, 62, 815. (30) Wiebe, R.; Gaddy, V. L. J. Am. Chem. Soc. 1941, 63, 475. (31) North, N. A. J. Phys. Chem. 1973, 77, 931.
Figure 5. Interfacial tension between pure CO2 and water as a function of pure CO2 pressure.39,40
excess adsorption where the isothermal compressibility is large, as discussed in greater detail below. For CO2 pressures above 7 MPa (activities above unity), γCW is well below γSW. The interfacial tension between CO2 and styrene oligomer (average molar mass ) 1850) is 2.2 dyn/cm at 45 °C and 20 MPa. Therefore, CO2 will be adsorbed preferentially at the interface to lower the overall γ between the latex mixture and water, according to the Gibbs adsorption equation. At the center of the latex particle, the CO2 concentration may be expected to be near the equilibrium value in bulk PS. It may be perturbed slightly by the presence of a small amount of water. At the particle-water interface, a surface excess of CO2 is present, which lowers the overall γ. At 25 °C and a CO2 activity of unity, the radius of the latex increases by 4 nm more than that expected from the swelling of bulk PS, based on the data in Figure 3. This result suggest that an interfacial region approximately 4 nm thick is present containing PS, CO2 and water. Since a thickness of 4 nm is on the order of the radius of gyration of the PS chain, this explanation is physically reasonable. The concept of enhanced swelling of a polymer due to a surface excess of CO2 is supported by recent measurements of the surface adsorption of CO2 into thin films of PS.33 Although water was not present, these experiments provide useful information concerning the interfacial activity of CO2 at the PS-CO2 interface. The Gibbs excess adsorption was measured with a quartz crystal microbalance with a new technique to eliminate the effect of buoyancy.33 It was determined by measuring the change in frequency of a crystal which was covered with thin PS films of varying thickness. At the point f/fsat ) 1, the measured amount of CO2 adsorbed onto PS is about 4 × 10-2 g/m2 or 0.002 nm2/molecule, far more than a monolayer. The adsorption area for a CO2 monolayer is 0.2 nm2/molecule.34 Thus the Gibbs excess adsorption of CO2 on PS is substantial for thin films, which is consistent with the above conclusion that this factor can play an important role on the enhanced swelling for the latex particles. For the latex swelling isotherm, a weak local maximum in the form of a protrusion is evident at an activity near (32) Harrison, K. L.; Johnston, K. P.; Sanchez, I. C. Langmuir 1996, 12, 2637-2644. (33) Otake, K.; Miura, K.; Kurosawa, S.; Sako, T.; Sugeta, T.; Nakane, A.; Sato, M.; Hongo, T. In preparation. (34) Kagaku Binran; Japan, C. S. o., Ed.; Maruzen: Tokyo, 1993.
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unity, which is near the critical point of CO2. This maximum occurs in the same region where γCW goes toward zero. Here the surface excess of CO2 is the largest and exhibits cusplike behavior, as has been shown experimentally35 and theoretically.36,37 The surface excess is defined by
Γex )
∫0∞(F(z) - F) dz
(9)
where F(z) is the molar density of the fluid at a distance z from the surface of the solid. Below the critical pressure region, the adsorbed layer increases in thickness faster than the bulk density increases, causing a rapid increase in Γex.37 At higher pressures, F becomes closer to the average F(z) and Γex decreases. The unusually large excess adsorption in the near-critical region likely produces the local maximum in the swelling behavior. (35) Findenegg, G. H. In Fundamentals of Adsorption; Myers, A. L., Belfort, G., Eds.; Engineering Foundation: New York, 1983; p 207. (36) O’Brien, J. A.; Randolph, T. W.; Carlier, C.; Ganapathy, S. AIChE J. 1993, 39, 1061-1071. (37) Rangarajan, B.; Lira, C. T.; Subramanian, R. Am. Inst. Chem. Eng. J. 1995, 41, 838-845. (38) Wissinger, R. G.; Paulaitis, M. E. J. Polym. Sci.: Part B: Polym. Phys. 1987, 25, 2497-2510. (39) Chun, B.-S.; Wilkinson, G. T. Ind. Eng. Chem. Res. 1995, 34, 4371-4377. (40) Harrison, K.; Johnston, K. P. 1996, In preparation.
Conclusions Liquid CO2 swells PS latex spheres in water about 60% more than bulk PS. The greater swelling for the PS latex may be attributed to the adsorption of CO2 at the PSwater interface which lowers the overall interfacial tension. Upon swelling, this lowering of the interfacial tension caused by adsorbed CO2 overcomes the otherwise unfavorable increase in interfacial area. On the basis of the enhanced swelling, the thickness of this interfacial region containing PS, carbon dioxide, and water is approximately 4 nm, which is on the order of the radius of gyration of a PS chain. Factors which cannot account for the enhancement in swelling include the sorption of water into the core of the latex and the change in pH due to carbonic acid. In the future particles of different initial diameters could be studied to further characterize the role of interfacial adsorption. A modest local maximum in the swelling, which is observed near an activity of unity, is likely due to the large Gibbs excess adsorption of CO2 near its critical point. Acknowledgment. We gratefully acknowledge support from NSF (CTS-9218769), the Texas Advanced Technology Program (3658-198), the Separations Research Program at The University of Texas, and the Japanese government for a fellowship to K.O. We thank K. Harrison, S. Mawson, M. O’Neill, and M. Yates for useful discussions. LA960855I
