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Solute Diffusion in Associative Copolymer Solutions Agnes K. Ho,†,§ Lev E. Bromberg,† Andrea J. O’Connor,‡ Jilska M. Perera,‡ Geoff W. Stevens,‡ and T. Alan Hatton*,† Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, and Department of Chemical Engineering, University of Melbourne, Victoria 3010, Australia Received September 11, 2000. In Final Form: March 20, 2001 Fluorescence recovery after photobleaching was used to study the diffusion of water-soluble solutes in aqueous solutions of an associative polymer, poly(ethylene oxide)-b-poly(propylene oxide)-b-poly(ethylene oxide)-g-poly(acrylic acid) (Pluronic-PAA). Above the critical micellization temperature (CMT), the PluronicPAA polymers form micellar aggregates that serve as cross-links for gelation of the polymer solution at these temperatures; the transition from no gel to complete gelation occurs over a 10 °C temperature range beginning at the CMT. The apparent diffusion coefficients of small hydrophobic fluorescent dyes decreased over the gel transition region as a portion of the dye present was immobilized within the hydrophobic cores of the micellelike aggregates, whose concentration increased with increasing temperature. A small effect on hydrophilic probes was observed in the transition region, but the diffusion characteristics once the gel was formed were those that would have been anticipated had there been no gelling. Diffusion of rigid spheres (proteins) depended on the Pluronic-PAA solution structure and could be explained qualitatively by the obstruction theory relating motion of the proteins in the interstices between impenetrable micellar aggregates to the aggregate volume fraction. Diffusion of flexible coils (dextrans) in Pluronic-PAA undergoing sol-gel transition corresponded to the simple scaling prediction D ∼ N0-1/2 (where N0 is the number of monomer units) afforded by the Zimm model for solutes of radius of gyration much smaller than the effective mean pore size in the gels.
Introduction The diffusion of solutes in polymer solutions and gels has been studied quite extensively over the years, both experimentally and theoretically,1-3 motivated in part by the numerous applications of hydrogels in fields such as chromatography, superabsorbency, and drug delivery. Much of the work in this area has been on diffusion within permanently cross-linked hydrogels, however, and relatively few studies have been reported on solute diffusion in aqueous systems undergoing thermoreversible solgel transitions, which is the topic of this communication. Among the most studied of the thermoreversible gelling systems is the family of triblock copolymers of poly(ethylene oxide) (PEO) and poly(propylene oxide) (PPO) (Pluronic block copolymers) which undergo a very pronounced viscosification upon heating because of the formation of micelles that pack in a cubic lattice to form a gel-like medium under well-defined concentration and temperature conditions.4-11 The sol-gel transition behavior of Pluronic block copolymers has been utilized for †
Massachusetts Institute of Technology. University of Melbourne. § Present address: Department of Chemical Engineering, University of Melbourne, Victoria 3010, Australia. ‡
(1) Doi, M.; Edwards, S. F. The Theory of Polymer Dynamics; Oxford University Press: Oxford, 1986. (2) De Gennes, P.-G. Scaling Concepts in Polymer Physics; Cornell University Press: Ithaca, NY, 1979. (3) Baumgartner, A.; Muthukumar, M. Adv. Chem. Phys. 1996, 94, 625. (4) Chen-Chow, P.-C.; Frank, S. G. Int. J. Pharm. 1981, 8, 89. (5) Gilbert, J. C.; Hadgraft, J.; Bye, A.; Brookes, L. G. Int. J. Pharm. 1986, 32, 223. (6) Chi, S. C.; Jun, H. W. J. Pharm. Sci. 1991, 80, 280. (7) Juhasz, J.; Lenaerts, V.; Raymond, P.; Ong, H. Biomaterials 1989, 10, 265. (8) Wu, C.; Liu, T.; Chu, B. Electrophoresis 1998, 19, 231. (9) Liang, D.; Chu, B. Electrophoresis 1998, 19, 2447. (10) Wu, C.; Liu, T.; Chu, B.; Schneider, D. K.; Graziano, V. Macromolecules 1997, 30, 4574.
controlled drug delivery because drugs can be conveniently formulated in an aqueous solution and then have a prolonged retention time in a gel when administered into the body.12,13 Graft copolymers of Pluronic block copolymers and poly(acrylic acid) (PAA) (Pluronic-PAA copolymers)14-33 also undergo a reversible sol-gel transition similar to the (11) Hadden, D. A.; Rill, R. L.; McFaddan, L.; Locke, B. R. Macromolecules 2000, 33, 4235. (12) Miyazaki, S.; Ohkawa, Y.; Takada, M.; Attwood, D. Chem. Pharm. Bull. 1992, 40, 2224. (13) Bhardwaj, R.; Blanchard, J. J. Pharm. Sci. 1996, 85, 915. (14) Bromberg, L.; Lupton, E. C.; Schiller, M. E.; Timm, M. J.; McKinney, G. W.; Orkisz, M.; Hand, B. Int. Patent Appl. WO 97/00275, 1997. (15) Bromberg, L.; Orkisz, M.; Roos, E.; Ron, E. S.; Schiller, M. J. Controlled Release 1997, 48, 305. (16) Bromberg, L. E.; Mendum, T. H. E.; Orkisz, M. J.; Ron, E. S.; Lupton, E. S. Proc. Polym. Mater. Sci. Eng. 1997, 76, 273. (17) Orkisz, M. J.; Bromberg, L.; Pike, R.; Lupton, E. C.; Ron, E. S. Proc. Polym. Mater. Sci. Eng. 1997, 76, 276. (18) Bromberg, L. E.; Orkisz, M. J.; Ron, E. S. Polym. Prepr. (Am. Chem. Soc., Div. Polym. Chem.) 1997, 38, 626. (19) Bromberg, L. E.; Ron, E. S. Adv. Drug Delivery Rev. 1998, 31, 197. (20) Bromberg, L. Langmuir 1998, 14, 5806. (21) Bromberg, L. Macromolecules 1998, 31, 6148. (22) Bromberg, L. J. Phys. Chem. B 1998, 102, 1956. (23) Bromberg, L. J. Phys. Chem. B 1998, 102, 10741. (24) Bromberg, L. Ind. Eng. Chem. Res. 1998, 37, 4267. (25) Bromberg, L. E.; Goldfeld, M. G. Polym. Prepr. (Am. Chem. Soc., Div. Polym. Chem.) 1998, 39, 681. (26) Bromberg, L. Polym. Prepr. (Am. Chem. Soc., Div. Polym. Chem.) 1999, 40, 616. (27) Huibers, P. D. T.; Bromberg, L. E.; Robinson, B. H.; Hatton, T. A. Macromolecules 1999, 32, 4889. (28) Bromberg, L. E.; Barr, D. P. Macromolecules 1999, 32, 3649. (29) Bromberg, L.; Salvati, L. Bioconjugate Chem. 1999, 10, 678. (30) Bromberg, L.; Magner, E. Langmuir 1999, 15, 6792. (31) Bromberg, L.; Temchenko, M. Langmuir 1999, 15, 8627. (32) Bromberg, L.; Temchenko, M.; Colby, R. H. Langmuir 2000, 16, 2609. (33) Ron, E. S.; Bromberg, L.; Luszak, S.; Kearney, M.; Deaver, D. R.; Schiller, M. Proc. Int. Symp. Controlled Release Bioact. Mater. 1997, 24, 407.
10.1021/la001301p CCC: $20.00 © 2001 American Chemical Society Published on Web 05/12/2001
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solution structure under the dilute Pluronic-PAA concentrations used here. Experimental Section
Figure 1. Polymer organization below and above the gel transition temperature, based on SANS analysis (ref 27).
transitions observed in Pluronic solutions.20,21,23 However, unlike Pluronic copolymers, the Pluronic-PAA is a high molecular weight species (MW > 105 Da) which, uniquely, exhibits gelation even in semidilute solutions.20 This gelation coincides with the formation of uniformly spaced micellelike aggregates through the entropy-driven aggregation of the PPO segments above a certain critical micellization temperature.27,28 In each of these aggregates, which act as physical cross-linkers for gelation, the dehydrated chains of PPO form a spherical core, surrounded by a more hydrated layer of PEO segments (the “inner corona”) and ionized PAA chains (the “expanded corona”), as illustrated schematically in Figure 1. Pluronic-PAA copolymers have been shown to be effective in topical drug delivery,15,16,19,33 and the transport of hydrophobic solutes such as pyrene and steroid hormones in Pluronic-PAA systems has been shown to depend on the release rate from hydrophobic PPO-rich domains.30 The diffusion of water-soluble solutes in such solutions has not yet been explored in detail, however, despite some interesting in vivo results.19,33 The present paper addresses this problem. The diffusion of watersoluble fluorescent species such as fluorescein and its derivatives and labeled proteins and dextrans of different molecular weights was studied using fluorescence recovery after photobleaching (FRAP), a technique which has found extensive application in other studies on the diffusion of solutes in concentrated polymer solutions34-39 and gels.40-48 We show that the diffusional behavior of small solutes depends on their hydrophobicity and extent of partitioning to the micellar aggregates when gelation occurs. Larger proteins are shown to be restricted in their motion through the gels, whereas flexible polymers are unaffected by the (34) Wattenbarger, M. R.; Bloomfield, V. A.; Bu, Z.; Russo, P. S. Macromolecules 1992, 25, 5263. (35) Bu, Z.; Russo, P. S. Macromolecules 1994, 27, 1187. (36) Kaufman, E. N.; Jain, R. K. Biophys. J. 1994, 60, 596. (37) Tinland, B.; Borsali, R. Macromolecules 1994, 27, 2141. (38) De Smedt, S. C.; Lauwers, A.; Demeester, J.; Engelborghs, Y.; De Mey, G.; Du, M. Macromolecules 1994, 27, 141. (39) Bryers, J. D.; Drummond, F. Biotechnol. Bioeng. 1998, 60, 462. (40) Mustafa, M. B.; Tipton, D.; Russo, P. S. Macromolecules 1989, 22, 1500. (41) Moussaoui, M.; Benlyas, M.; Wahl, P. J. Chromatogr. 1991, 558, 71. (42) Moussaoui, M.; Benlyas, M.; Wahl, P. J. Chromatogr. 1992, 591, 115. (43) Johnson, E. M.; Berk, D. A.; Jain, R. K.; Deen, W. M. Biophys. J. 1996, 70, 1017. (44) Laurent, T. C. Biochim. Biophys. Acta 1967, 136, 199. (45) Johnson, E. M.; Berk, D. A.; Jain, R. K.; Deen, W. M. Biophys. J. 1995, 68, 1561. (46) Boyer, P. M.; Hsu, J. T. AIChE J. 1992, 38, 259. (47) Pluen, A.; Netti, P. A.; Jain, R. K.; Berk, D. A. Biophys. J. 1999, 77, 542. (48) Berk, D. A.; Yuan, F.; Leunig, M.; Jain, R. K. Biophys. J. 1993, 65, 2428.
Materials. Pluronic F127 NF was kindly donated by BASF Corp. (Mount Olive, NJ) and used without further treatment. It has the following characteristics: formula, EO100PO65EO100; nominal molecular weight, 12 600; molecular weight of PPO segment, 3780; 70 wt % of EO; cloud point above 100 °C. Poly(ethylene oxide)-b-poly(propylene oxide)-b-poly(ethylene oxide)g-poly(acrylic acid) (CAS no. 186810-81-1) was synthesized by dispersion/emulsion polymerization of acrylic acid along with the simultaneous grafting of poly(acrylic acid) onto the Pluronic backbone as described in detail elsewhere.24 In this work, we refer to the ensuing copolymer as Pluronic-PAA. The polymer of weight-average molecular mass 4 × 106 Da and polydispersity 6.5 consisted of 45% Pluronic F127 and 55% poly(acrylic acid) as determined by FTIR and NMR spectroscopy.24 Fluorescein, sodium salt (water content, 7.5%), and dextrans labeled with fluorescein isothiocyanate (FITC) (nominal molecular weights 4400, 10 000, and 19 000; dye content, 0.008 mol dye/mol) were obtained from Sigma Chemical Co. FITC-labeled bovine serum albumin (BSA) (5.6 mol dye/mol), FITC-labeled concanavalin A (FITC-Con A) (6.4 mol dye/mol), and FITC-labeled dextran (MW 70 000, 8.3 mol dye/mol) were all obtained from Molecular Probes, Inc. (Eugene, OR) and used as received. Fluorescein diactetate (Fl-Ac2) (dye content, 98%) was obtained from Aldrich Chemical Co. All other chemicals, gases, and organic solvents of the highest purity available were obtained from commercial sources. Procedures. Pluronic-PAA solutions (2 w/w %) were prepared by weighing the appropriate amount of polymer powder, neutralizing with an equal mass of 5 M NaOH, and dissolving in Milli-Q water. The solutions were stirred overnight and kept in an ice bath (4 °C) to aid dissolution. The final solution pH was 6.95 ( 0.6. Fluorescent solutes were then introduced into the polymer solutions, which were again left stirring overnight in an ice bath. The concentration of each solute varied between 1 and 50 µM in most cases (400 µM for Fl-Ac2) depending on their ease of photobleaching in the FRAP experiments. All solutions containing fluorescent probes were stored in sealed vials and wrapped in aluminum foil to protect them from light. FRAP Apparatus and Measurement. A schematic diagram of the FRAP apparatus is shown in Figure 2. The entire system was automated and controlled through LabVIEW and C programs developed in-house. The light source was a Stabilite-2017 argonion continuous-wave laser (a) from Spectra-Physics (Mountain View, CA). A beam splitter (b) split the laser beam into a strong beam (c) and an attenuated beam (k). The strong beam traveled through a shutter (d), which opened only when a predetermined region in the sample cell was to be photobleached. The width of the beam was controlled by a long focal length converging lens (e). The diffusion cell (r) was an anodized aluminum block with a rectangular cavity in the middle to allow insertion of a quartz cuvette. Temperature control was achieved by circulating water, chilled or heated to the desired temperature using a Neslab RTE110 water bath, through channels in the metal block. The cuvette was of path length 2 mm, which was sufficiently small that it was within the depth of field of the microscope (i), giving a twodimensional projection of the contents of the cell. For bleaching, the beam was scanned horizontally back and forth across the cell by means of a computer-controlled translation stage (f). This effectively reduced the two-dimensional diffusion process to one dimension, provided that the distance across which the beam scanned was large relative to the area of observation, and the time taken for a scan was small relative to the diffusional time scale of the system. By use of multiple scans, the extent of bleaching could be varied for any given laser power. After photobleaching, the other beam (k) passed through a shutter (n), which opened at predetermined time intervals to illuminate the cell when a concentration measurement was required. To ensure a more uniform illumination field, the beam passed through two beam expanders (p and q). To avoid further bleaching of the fluorophores during observation, the beam intensity was reduced before it reached the sample cell by passing the beam through a neutral density filter in the rotating filter wheel (l). A dichroic filter (h) with a wavelength cutoff of 505 nm,
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Figure 2. Schematic diagram of the FRAP experimental setup. See text for details. obtained from Omega Optical (Brattleboro, VT), was placed in front of the diffusion cell. This reflected the 488 nm wavelength light from the laser onto the diffusion cell for photobleaching when the bleaching shutter (d) was opened and transmitted the resulting fluorescence emission at the longer wavelength of 512 nm for recovery monitoring when the observation shutter (n) was opened. The transmitted signals entered the epi-illuminated microscope (i) where the images were captured by a CCD camera (j) and the system relaxation was recorded. To account for temporal variations in beam intensity and therefore to enhance the quality of the images obtained, part of the weak beam was split by an optical flat (m). This weak beam passed through two beam expanders in sequence (s and t) and was monitored by a second CCD camera (u). Images captured by both cameras were sent to the frame grabber board (v) (Data Translation, Inc., Marlboro, MA) installed on an IBM PC for signal digitizing and processing. Pluronic-PAA solutions with the appropriate fluorescent solute were loaded into the quartz cuvette at low temperatures to ensure that the polymer solution remained in the liquid state during the injection. The water bath was set at different temperatures between 15 and 40 °C for each experiment, giving a solution temperature range of 15.5-38.1 °C, as measured using a thermocouple. The contents of the cell were allowed to equilibrate, and the cell was placed in the object plane of the microscope. The laser was switched on at a fixed power, typically 1.0-1.9 W, and the experiment commenced. On the diffusion cell, the power was reduced to 120-220 and 2-16 mW for the bleaching and monitoring beams, respectively, after passage through the optical components. Input parameters such as the number of scans, the size (length) of the scan, and image acquisition times were entered into the computer software, and the LabVIEW and C programs were activated. Nine images of the fluorescence recovery, in addition to the prebleach image, were stored in the frame grabber. The measurements were repeated in triplicate. The standard error did not exceed 15%. The program subtracted background noise and processed the images. The diffusion coefficient for any particular run was obtained by selecting that value that minimized the sum of squares of the deviations between model predictions and all the experimental data points collected over the time course of the experiment. The theoretical solute concentration profiles were calculated by numerical integration of the diffusion equation,
∂c ∂2c )D 2 ∂t ∂x
with the initial condition given by the concentration profiles determined experimentally immediately following the bleaching process. The far-field boundary conditions demanded that the concentrations remained unchanged far from the bleached zone, that is, c(x ) (∞) ) c0, the initial prebleach fluorophore concentration. Light Scattering Experiments. Dynamic light scattering experiments were performed with a Brookhaven Instruments BI-200SM goniometer, a BI-9000 correlator, and a Spectra Physics He-Ne model 127 laser operating at a scattering angle of θ ) 60° and a wavelength of incident light of λ ) 633 nm at a power of 35 mW as described in detail previously.49 The intensity of the slow modes (corresponding to large scatterers with correlation lengths above 1000 Å) at temperature T was related to the intensity of the slow modes I0 measured at 26 °C, and the resulting relative intensity I/I0 was used as an arbitrary temperature-dependent indication of the extent of aggregation. Rheological Experiments. Rheological measurements were performed using a controlled stress Rheolyst series AR1000 rheometer (TA Instruments, New Castle, DE) with a cone and plate geometry system (cone: diameter, 4 cm; angle, 2°, truncation, 57 µm) equipped with a solvent trap. Temperature control (internal resolution 0.016 °C) was provided by two Peltier plates. Equilibrium flow measurements were conducted in a stepped ramp mode with the shear stress as a controlled variable at a constant shear rate of 0.12 s-1.
Results and Discussion Viscosification and the Formation of Large Aggregates. The viscosity of the Pluronic-PAA solutions increased dramatically with temperature, as shown in Figure 3. This increase coincided directly with the formation of large aggregates as inferred from the increase of the relative intensity of the corresponding light scattering component over the same temperature range; the two curves superimpose when appropriately scaled, presumably because both effects were due to the same phenomenon, that is, the formation of aggregates by the entropy-driven collapse of PPO segments of PluronicPAA.20,23 The micellelike aggregates serve as cross-links bridging Pluronic-PAA macromolecules as shown schematically in Figure 1. The critical micellization temperature (CMT) and the gelation threshold temperature (Tgel)
(1) (49) Bromberg, L.; Temchenko, M. Langmuir 1999, 15, 8633.
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Figure 3. Effect of temperature on equilibrium viscosity (filled points) and relative intensity of large scatterers (open points) of 2 w/w % Pluronic-PAA solution (pH 7.0). For other parameters, see Experimental Section.
have been established to be the same at about 17-19 °C for a 2% Pluronic-PAA solution, depending on the molecular weight of Pluronic-PAA.21 Diffusion of Dyes. A series of fluorescence recovery profiles determined at 10 s intervals following the bleaching of a fluorescein solution is shown in Figure 4a. In this example, heating of the solution during the bleaching process caused buoyancy-induced free convection to set in, as is evident from the drift of the profiles to the right over time. The position of the profile minimum is shown as a function of time in Figure 4b, from which the velocity, given by the slope of the line passing through these points, is seen to have been constant during this experiment. The effect of the convection on the evolution of the concentration profiles can be removed by adopting a Lagrangian frame of reference and shifting the profiles to align their minima, as shown in Figure 4c. These curves show only the diffusive component of the profile evolution and are described well by the classical diffusion description given by Fick’s second law. A reliable value of the diffusion coefficient was extracted from these results by fitting the numerical solution of Fick’s law (eq 1) to the experimental profiles; the model fits are shown as solid lines in Figure 4c. In many of the experiments, lower levels of bleaching (fewer scans of the bleaching beam) were used such that the heating of the solution was insufficient to induce convection and the profiles obtained resembled those shown in Figure 4c. The effect of temperature on the diffusion coefficients of sodium fluorescein and its diacetate derivative in 2% Pluronic-PAA solutions is shown in Figure 5 together with the viscosity variation over the same temperature range to indicate the transition region. The diffusion coefficients obtained for fluorescein in 2% Pluronic-PAA at room temperature are about 10% lower than our measured value in pure water (Dav ≈ 2.8 × 10-6 cm2/s at 23 °C) and close to the literature value at the same temperature (D ≈ 2.6 × 10-6 cm2/s).48 For both fluorophores, there is an initial increase in the diffusion coefficient with temperature, followed by a decrease in this parameter over the gelation transition region. The nature of this decrease, which is due to the changing structure of the polymer solution over this region, is different for the two dyes. Beyond the transition region, the diffusion coefficients again increase, with approximately the same rate of change with temperature as observed below the transition region. For the hydrophilic sodium fluorescein, the diffusion coefficients at the higher temperatures are essentially those obtained by extrapolation of the low-temperature data, indicated by the dashed line. The results for the hydrophobic fluorescein diacetate at the higher temperatures are significantly lower, however, than would be
Figure 4. Fluorescence recovery profiles following bleaching of an aqueous 5 µM sodium fluoroscein solution at neutral pH using seven scans with 10.7% transmission and 0.6 W laser power. (a) Direct experimental measurements showing effect of free convection on evolution of the profiles. (b) The position of the profile minimum as a function of time; the slope gives the solution velocity. (c) The measured profiles corrected for the velocity drift to show only the diffusive component of the profile development. The solid lines are the fitted curves based on Fick’s law (eq 1).
Figure 5. Effect of temperature on diffusion coefficients of sodium fluorescein (open points) and fluorescein diacetate (filled points) in 2 w/w % Pluronic-PAA solution (pH 7.0). The temperature-dependent viscosity profile is shown for comparison as a solid line. The solid lines indicate the trends in the data and have no theoretical basis.
obtained by such an extrapolation. This difference can be attributed to the immobilization of a certain fraction of the dye within the hydrophobic cores of the aggregates,
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which did not contribute to the overall diffusion of the solute through the gel matrix. Indeed, the measured diffusion coefficient can be approximated by the simple expression
D ) ϑD0 + (1 - ϑ)Dm where ϑ is the mobile fraction of solute in the aqueous phase having diffusion coefficient D0 and Dm is the diffusion coefficient of the micelles, or aggregates, containing the remaining fraction of the dye. For the gel phase, we can assume that the aggregates are essentially immobile and hence do not contribute to the diffusional transport of the fluorophores to the bleached zone. Thus, the measured diffusion coefficient is just D ) ϑD0. From the linear extrapolation of the low-temperature data to higher temperatures, we can estimate the diffusion coefficient that would have been obtained had there been no gelling, or formation of hydrophobic scattering centers. The fraction ϑ is then obtained from the ratio of the actual diffusion coefficient (∼2 × 10-6 cm2/s at 34 °C) to the extrapolated value of ∼3 × 10-6 cm2/s at the same temperature. This result suggests that approximately 30% of the total solute is associated with the micelles. About 70% of the polymer is itself in aggregated form (the remainder being in the “outer corona” region), and of this about 30% is PPO, so the effective volume of the active solubilizing component in the system (i.e., micellized PPO) is approximately 0.4% (0.7 × 0.3 × 2%). From these values, we can estimate that the micelle/water partition coefficient for the fluorescein diacetate is approximately 130 (for comparison, the octanol/water partition coefficient, P, for this dye is ∼3000; log P ) 3.5151). Over the transition region, the diffusion coefficient for the diacetate decreases steadily, correlating directly with the viscosity increase and hence with the formation and growth of large micellar aggregates; that is, the fraction ϑ decreases steadily as the volume of the solubilizing aggregates increases. The behavior exhibited by the hydrophilic sodium fluorescein dye (log P ) -0.6751) is somewhat different. This dye does show a decrease in the diffusion coefficient in the transition region, but the onset of this decrease is delayed relative to that of the more hydrophobic diacetate, the decrease itself is more abrupt and not as extensive, and it occurs only over a narrow temperature range. With further increases in temperature, we recover the diffusion coefficients that would be anticipated if there were no gel formation at all, based on the extrapolation of the lowtemperature data. We surmise that there is some interaction of the dye with either the PEO or PPO segments of the Pluronic block copolymers (hence the lower diffusion coefficients than those obtained in pure water). This results in a decrease in the transport of the dye in the middle of the transition region where these segments are beginning to be restrained in their movement because of micelle formation. With further temperature increases, the micelles become more compact as the polymers are dehydrated and the dye is expelled from the micellar inner corona region, and most of the dye reports to the aqueous phase where its diffusion is once again relatively unhin(50) Nystro¨m, B.; Kjøniksen, A.-L. Langmuir 1997, 13, 4520. (51) Octanol-water partition coefficients (log P) were obtained from the LogKow (KowWin) program from Environmental Science Center (ESC), Syracuse Research Corporation (SRC), Syracuse, NY. This program is available on the Internet (http://esc-plaza.syres.com/ interkow/onlinedb.htm). Calculations are based on an atom/fragment contribution approach, and the methodology is described in: Meylan, W. M.; Howard, P. H. J. Pharm. Sci. 1995, 84, 83. For comparison, log P values for hydrophobic molecules pyrene and DPH are 4.93 and 6.06, respectively.
Figure 6. Temperature dependencies of relative diffusion coefficients (D/D0) of proteins in 2 w/w % Pluronic-PAA solution (pH 7.0). Here, D0 is the diffusion coefficient of the protein in water at a given temperature calculated from the StokesEinstein equation. Data for FITC-BSA and FITC-Con A are shown by filled and open points, respectively. The data points show experimental data, and the corresponding solid lines represent model calculations as described in the text. The temperature-dependent viscosity profile is shown for comparison as a solid line.
dered. The diffusion coefficient is close to that in the pure water phase. Both below and above the transition region, the structure of the polymer solution through which the solute diffuses remains unchanged with changing temperature, and that fraction of the solute that is not immobilized by interactions with the aggregates can be considered essentially to be moving through water. In this case, the Stokes-Einstein relation
D0 ) kT/(6πηRH)
(2)
can be used to estimate solute diffusion coefficients for the mobile fraction of the probe solute, where k is the Boltzmann constant, T is the absolute temperature, η is the local viscosity (not the solution bulk viscosity) of the medium through which the solute is diffusing (essentially water), and RH is the hydrodynamic radius. In particular, this equation predicts that the temperature dependency should be the same above the transition region as it is below this region, as is observed. Indeed, this observation was the basis for the extrapolations indicated in Figure 5. Diffusion of Proteins. Diffusion coefficients for the two proteins BSA and concanavalin A in Pluronic-PAA solutions are shown as a function of temperature in Figure 6, again with the viscosity variations over the same temperature range as a reference. These results were normalized by the protein diffusion coefficients in water at the same temperatures to decouple specific temperature effects from the effects of the structure of the polymer gels on the protein transport. It is evident that over the transition region where the gel begins to form the relative protein diffusion coefficients decrease. In contrast to the fluorescein diacetate case, this effect is attributed not to partitioning of the proteins to the hydrophobic cores of the micellar-type aggregates that form at these temperatures but rather to hindered diffusion effects as the proteins negotiate a more torturous diffusional path through the structured gel. We describe this effect using the obstruction model, in which we assume that the gel acts as a sieve, allowing passage of a protein only in the “voids” between the dense aggregates. Such a model is especially appealing as we can verify it through the structural parameters of the Pluronic-PAA solution revealed by our previous small-angle neutron scattering (SANS) study27 in which it was shown that at temperatures well above the CMT, the Pluronic-PAA forms a network
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of relatively monodisperse scattering aggregates, with an inner corona diameter of d ) 120 Å and a distance between the aggregates of s ) 470 Å (data for 2% Pluronic-PAA solution).27 The volume fraction (packing factor) of the impenetrable element in solution (φ) can be calculated as:52
φ ) φpd3/s3
(3)
where φp ) x2π/6 = 0.74 is the packing factor under a tight tetrahedral or rhombohedral packing arrangement. Using the SANS data, we obtain φ ) 0.0123 for a 2% Pluronic-PAA solution at temperatures well above the CMT (T ) 35-45 °C). At lower temperatures within the transition region, the large scatterers are not as well developed and therefore provide less of a hindrance to the diffusion of the proteins. Because the scattering is assumed to be directly due to the large aggregates, we can approximate the relative contribution of these large scatterers to φ to be proportional to the total scattering intensity, that is, φ/φ40°C ) I/I40°C ) R(T). Therefore, according to our obstruction model, the relationship between the temperature-dependent diffusion coefficient in the Pluronic-PAA (D) and in water (D0) can be expressed as
D/D0(T) ) [1 - R(T)] + (D/D0)cR(T)
(4)
where (D/D0)c ) exp(-0.84R1.09) is the reduction in the solute diffusivity predicted by the widely used obstruction theory.53 Here, R ) φ[(rs + rf)/rf)]2 , and rs and rf are the radii of the solute and the fibril of the polymer constituent, respectively.54 Using R(T) found from the light scattering data (Figure 3), rf ) 6.8 Å obtained from light scattering measurements as the hydrodynamic radius based on the number-average intrinsic viscosity of Pluronic-PAA,23 and rs of 36.3 Å for BSA,54 we were able to obtain a good a priori prediction of the relative diffusivity of this protein as determined in our FRAP experiments; this prediction is shown as a solid line in Figure 6. Concanavalin A, however, consists of two (dimer) or four (tetramer) identical protomers of mean molecular weight 25 000, folded into domelike structures (42 × 40 × 39 Å) as determined by X-ray crystallography,55,56 and thus it was not possible to specify a unique size for this protein in solution. The dimers can be treated as anisotropic objects, approximately 84 × 40 × 39 Å in size, and the tetramers can be treated as isotropic objects of about 80 Å in diameter. At pH 7.0, as in our experiments, concanavalin A is largely tetrameric. Such ambiguity in determining rs values for concanavalin A necessitated selecting that value of the protein size that allowed for the best fit of the model (solid line shown in Figure 6) to the experimental data; a value of rs ) 60 Å was found to be appropriate. The expression for (D/D0)c adopted from the work of Johansson et al.53 was developed for the diffusion of spherical solutes in a permanent gel and does not account for the specific packing geometry of the Pluronic-PAA micelles. Although there have been numerous attempts at developing obstruction models for gels and these have been used successfully in predicting relative diffusivities of proteins in heterogeneous gels,54 (52) Patton, T. C. Paint Flow and Pigment Dispersion, 2nd ed.; Wiley: New York, 1979; pp 126-138. (53) Johansson, L.; Elvingston, C.; Lofroth, J.-E. Macromolecules 1991, 24, 6024. (54) Amsden, B. Macromolecules 1998, 31, 8382. (55) Gauthier-Manuel, B.; Gallinet, J. P. Langmuir 1997, 13, 2541. (56) Reeke, G. N.; Becker, J. W.; Edelman, G. M. J. Biol. Chem. 1975, 250, 1525.
Figure 7. Dependencies of the diffusion coefficients of dextrans on N0 at different temperatures in 2 w/w % Pluronic-PAA solution (pH 7.0). Here, N0 is defined as the nominal number of glucose units per dextran molecule. The solid line illustrates the dependence D ∼ N0-0.5 and is shown to guide the eye only.
such models accounting for the peculiarities of reversible gels are, at present, lacking. We believe, however, that the simple obstruction model described above is able to capture adequately the diffusional behavior of proteins in Pluronic-PAA gels and even account for the temperaturedependent aggregation using experimentally observed measures of this aggregation behavior. Transport of Dextrans. Whereas the diffusion of rigid molecules such as the proteins considered above depends on their hydrodynamic radius or molecular spherical radius (rs) and follows an obstruction model, the diffusion of flexible chains depends on the radius of gyration (Rg), determined via the persistence length, the number of monomers in the polymer chain (N0), and the intermonomer spacing.57,58 The diffusion of flexible polymer chains in gels also depends on the mean pore size (a) defined such that the volume between gel fibers is treated as a cylinder of radius a. The diffusion of polymer chains is separated into two regimes of behavior based on the chain length relative to pore size.1,2 According to the Zimm extension of the Rouse model,1 when Rg < a/2 the Gaussian chain diffuses in the gel as an ellipsoid with a diffusion coefficient D ∼ N0-1/2 in a θ solvent, and D ∼ N0-0.6 in a good solvent.57,58 When Rg > a/2, the diffusion is best described by the reptation theory,2 which considers movement of the polymer chain to be through a curvilinear motion along the macromolecule’s own contour, and yields a much steeper scaling exponent, D ∼ N0-2. Dextran is a typical random coil flexible polymer,59,60 in which approximately 95% of the glucose units are joined by 1,6-linkages. The remaining 5% are connected via 1,4-, 1,3-, and 1,2-linkages in short side chains.61 We have tested the above theoretical scaling predictions using dextrans as model compounds. Figure 7 shows the scaling exponent for the variation of the diffusion coefficient of dextrans with N0 (defined as the nominal number of glucose units in the dextran molecule) to be approximately -0.5, in agreement with the predictions of the Zimm extension of the Rouse model. The results are insensitive to temperature over the entire gel transition range indicating that the scattering centers that develop with increasing temperature do not affect the movement of these flexible chains through the gels. These results are consistent with (57) Sun, S. F. Physical Chemistry of Macromolecules; Wiley: New York, 1994; pp 201-207. (58) Pluen, A.; Netti, P. A.; Jain, R. K.; Berk, D. A. Biophys. J. 1999, 77, 542. (59) Smit, J. A. M.; van Dijk, J. A. P. P.; Mennen, M. G.; Daoud, M. Macromolecules 1992, 25, 3585. (60) Senti, F. R.; Hellman, N. N.; Ludwig, N. H.; Babcock, G. E.; Tobin, R.; Glass, C. A.; Lamberts, B. L. J. Polym. Sci. 1955, 17, 527. (61) Nordmeier, E. J. Phys. Chem. 1993, 97, 5770.
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the observation that water is a θ solvent for dextran, and the radius of gyration for the largest dextran used (70 000 Da), Rg ) 70 Å,62 is significantly smaller than the effective pore size, a/2 ) 230 Å. Conclusions The diffusion of water-soluble solutes ranging in molecular weight from 400 to 70 000 in semidilute aqueous solutions of an associative polymer, poly(ethylene oxide)b-poly(propylene oxide)-b-poly(ethylene oxide)-g-poly(acrylic acid) (Pluronic-PAA), was assessed using fluorescence recovery after photobleaching. The FRAP technique was shown to be useful in the study of solute transport as it requires only small sample volumes and is capable of distinguishing between diffusive and convective transport. The Pluronic-PAA solutions exhibited dramatic viscosification above their critical micellization temperatures that coincided with the appearance of large aggregates, as indicated by the light scattering intensity increase. The solute diffusion mechanism in the PluronicPAA copolymer solutions undergoing a sol-gel transition depends on the size, hydrophobicity, and conformation of the solutes. Diffusion coefficients of the small hydrophobic fluorescent dye, fluorescein diacetate, decreased with increasing gel formation owing to the immobilization of a fraction of the fluorophore by solubilization within the hydrophobic cores of the micellelike aggregates. Diffusion (62) Kloster, C.; Bica, C.; Rochas, C.; Samios, D.; Geissler, E. Macromolecules 2000, 33, 6372.
Ho et al.
of proteins depended strongly on the aggregation state of the Pluronic-PAA as reflected by the viscosity and scattered light intensity and can be explained qualitatively by the motion in the interstices between impenetrable aggregates. Using structural parameters of the aggregates obtained from the SANS study27 and the temperature dependence of the fractional volume of the aggregates obtained herein by light scattering, we obtained a satisfactory correlation between diffusion coefficients predicted by the obstruction theory53 and experimental values. Diffusion of dextrans in Pluronic-PAA appears to follow dependencies typically predicted by the Zimm model for flexible random coil polymers throughout the temperature range studied, consistent with the radius of gyration of the dextrans used being much smaller than the effective mean pore size in Pluronic-PAA gels. Acknowledgment. The authors thank Edward Browne for designing and constructing the FRAP apparatus and for his useful discussions on the operation of the equipment and Seif Fateen for checking some of the curve fitting results. Financial support for this work, in the form of an Australian Postgraduate Award and the Postgraduate Overseas Research Experience Award for A. Ho, and also funding from the A. R. C. Particulate Fluids Processing Special Research Center is gratefully acknowledged. L.E.B. is indebted to the late Professor Toyoichi Tanaka for generous help and useful discussions. LA001301P
