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Kinetics of Fusion of Polystyrene-b-poly(acrylic acid) Vesicles in Solution Amira A. Choucair, Annia H. Kycia, and Adi Eisenberg* Department of Chemistry, McGill University, 801 Sherbrooke Street West, Montreal, Quebec, H3A 2K6 Canada Received July 3, 2002. In Final Form: November 18, 2002 Polystyrene-b-poly(acrylic acid) vesicles prepared in dioxane/water mixtures are equilibrium structures that respond to changes in the solvent composition by changing their size. An increase in vesicle size can be induced by adding water and occurs by vesicle fusion, while a decrease in vesicle size involves vesicle fission and can be induced by decreasing the water content in the solvent mixture. In this study, the kinetics of increase in vesicle size were examined. We evaluate the relaxation times of the process and determine the effect of factors such as the water content in the solvent mixture, the extent of perturbation in the solvent composition, the initial polymer concentration, and the acrylic acid block length on the rates. After adding water, the fusion of vesicles in solution was followed by measuring the change in turbidity as a function of time, and the relaxation times were extracted from the resulting turbidity vs time plots. The results show that the kinetics of increase in vesicle size become progressively slower as the water content increases, while increasing the magnitude of perturbation (i.e., the amount of water added) results in faster rates. Increasing the initial polymer concentration or the acrylic acid block length changes vesicle size and vesicle concentration and causes an increase in the rate of vesicle fusion.
1. Introduction Amphiphilic block copolymers self-assemble in solvents selective for one of the blocks to form colloidal size aggregates or micelles.1-3 Block copolymer aggregates, like those prepared from small-molecule surfactants,4-13 can assume a range of different morphologies in dilute solutions, including spheres, rods, vesicles, large compound micelles, and others.14-31 In our group, block * To whom all correspondence should be addressed. E-mail:
[email protected]. (1) Tuzar, Z.; Kratochvil, P. Adv. Colloid Interface Sci. 1976, 6, 201. (2) Price, C. In Developments in Block Copolymers; Goodman, I., Ed.; Applied Science Publishers: London, 1982; Vol. 1, p 39. (3) Selb, J.; Gallot, Y. In Developments in Block Copolymers; Goodman, I., Ed.; Elsevier Applied Science Publishers: London, 1985; Vol. 2, p 27. (4) Couper, A. In Surfactants; Tadros, T. F., Ed.; Academic Press: London, 1984; p 19. (5) Israelachvili, J. N. In Surfactants in Solution; Bothorel, P., Ed.; Plenum Press: New York, 1986; Vol. 4, p 3. (6) Kunitake, T. In Surfactants in Solution; Bothorel, P., Ed.; Plenum Press: New York, 1986; Vol. 5, p 727. (7) Israelachvili, J. N. Intermolecular and Surface Forces, 2nd ed.; Academic Press: London, 1992. (8) Zana, R.; Talmon, Y. Nature (London) 1993, 362, 228. (9) Kaler, E. W.; Murthy, A. K.; Rodriguez, B. E.; Zasadzinski, J. A. Science 1989, 245, 1371. (10) Kakizawa, Y.; Sakai, H.; Nishiyama, K.; Abe, M.; Shouji, H.; Kondo, Y.; Yoshino, N. Langmuir 1996, 12, 921. (11) Morgan, J. D.; Johnson, C. A.; Kaler, E. W. Langmuir 1997, 13, 6447. (12) Regev, O.; Leaver, M. S.; Zhou, R.; Puntambekar, S. Langmuir 2001, 17, 5141. (13) Kakizawa, Y.; Sakai, H.; Yamaguchi, A.; Kondo, Y.; Yoshino, N.; Abe, M. Langmuir 2001, 17, 8044. (14) Antonietti, M.; Heinz, S.; Schmidt, M.; Rosenauer, C. Macromolecules 1994, 27, 3276. (15) Honda, C.; Sakaki, K.; Nose, T. Polymer 1994, 35, 5309. (16) Gao, Z.; Varshney, S. K.; Wong, S.; Eisenberg, A. Macromolecules 1994, 27, 7923. (17) Zhang, L.; Eisenberg, A. Science 1995, 268, 1728. (18) Yu, K.; Zhang, L.; Eisenberg, A. Langmuir 1996, 12, 5980. (19) Zhang, L.; Eisenberg, A. J. Am. Chem. Soc. 1996, 118, 3168. (20) Liu, G.; Qiao, L.; Guo, A. Macromolecules 1996, 29, 5508. (21) Prochazka, K.; Martin, T. J.; Webber, S. E.; Munk, P. Macromolecules 1996, 29, 6526. (22) Nagarajan, R. NATO ASI Ser., Ser. E 1996, 327, 121. (23) Zhang, L.; Bartels, C.; Yu, Y.; Shen, H.; Eisenberg, A. Phys. Rev. Lett. 1997, 79, 5034.
copolymer aggregates are usually prepared by first dissolving the copolymer in a solvent common for both blocks, such as dimethylformamide (DMF), tetrahydrofuran (THF), or dioxane, and then adding water, which is a poor solvent for the hydrophobic block, to induce selfassembly. The morphology and dimensions of the resulting aggregates are determined by a force balance among three contributions to the free energy: core-chain stretching, corona-chain repulsion, and interfacial tension between the core and the outside solution.32-34 Consequently, factors that alter the above balance, such as the relative block length,19,35-37 the water content in the solvent mixture,35,36,38 the nature and composition of the common solvent,39-41 the presence of additives (ions,32,33 surfactants,42 or homopolymer19), or the polymer concentration34-36 can be employed to control the aggregate shape and size.43 Vesicles, which constitute a major part of the block copolymer morphological phase diagram,36 are closed (24) Massey, J.; Power, K. N.; Manners, I.; Winnik, M. A. J. Am. Chem. Soc. 1998, 120, 9533. (25) Jenekhe, S. A.; Chen, X. L. Science 1998, 279, 1903. (26) Alexandridis, P.; Olsson, U.; Lindman, B. Langmuir 1998, 14, 2627. (27) Cameron, N. S.; Corbierre, M. K.; Eisenberg, A. Can. J. Chem. 1999, 77, 1311. (28) Won, Y.-Y.; Davis, H. T.; Bates, F. S. Science 1999, 283, 960. (29) Talingting, M. R.; Munk, P.; Webber, S. E.; Tuzar, Z. Macromolecules 1999, 32, 1593. (30) Harada, A.; Kataoka, K. Science 1999, 283, 65. (31) Discher, B. M.; Won, Y.-Y.; Ege, D. S.; Lee, J. C. M.; Bates, F. S.; Discher, D. E.; Hammer, D. A. Science 1999, 284, 1143. (32) Zhang, L.; Yu, K.; Eisenberg, A. Science 1996, 272, 1777. (33) Zhang, L.; Eisenberg, A. Macromolecules 1996, 29, 8805. (34) Zhang, L.; Eisenberg, A. Macromolecules 1999, 32, 2239. (35) Shen, H.; Eisenberg, A. Macromolecules 2000, 33, 2561. (36) Shen, H.; Eisenberg, A. J. Phys. Chem. B 1999, 103, 9473. (37) Won, Y.-Y.; Brannan, A. K.; Davis, H. T.; Bates, F. S. J. Phys. Chem. B 2002, 106, 3354. (38) Zhang, L.; Eisenberg, A. Polym. Adv. Technol. 1998, 9, 677. (39) Yu, Y.; Eisenberg, A. J. Am. Chem. Soc. 1997, 119, 8383. (40) Yu, Y.; Zhang, L.; Eisenberg, A. Macromolecules 1998, 31, 1144. (41) Li, Z.-C.; Shen, Y.; Liang, Y.-Z.; Li, F.-M. Chin. J. Polym. Sci. 2001, 19, 297. (42) Burke, S. E.; Eisenberg, A. Langmuir 2001, 17, 8341. (43) Choucair, A.; Eisenberg, A. Eur. Phys. J. E, in press.
10.1021/la026187k CCC: $25.00 © 2003 American Chemical Society Published on Web 01/18/2003
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spherical bilayers.7 The insoluble blocks constitute the vesicle wall, while the chains of the soluble block extend from the inner and outer surfaces into the solvent system. Recently, vesicles prepared from block copolymers have attracted the attention of several research groups.31,44-54 The interest in polymeric vesicles was motivated, in part, by the variety of their practical applications. In addition to their potential use as microreactors,55 environmental toxin sequesters, or drug delivery vehicles,46 block copolymer vesicles serve as a mimic for biological membranes.55 They are also attractive synthetic models for biological cells,56 since they can act as a reservoir, suitable for the encapsulation of proteins and other biologically active molecules, both in the bilayer region and in the vesicle interior.55,57 Moreover, polymeric vesicles are versatile structures that can be prepared in different sizes (ranging from tens of nanometers51,58 to few microns25,52,57,59), and in different media including aqueous,31,46,49,60 organic,44,45 and aqueous-organic mixtures.17,38,51,58,59 Of particular value in this connection is the ability to control vesicle size and properties by tailoring copolymer parameters (such as the relative block length59 or the chemical nature of the repeat unit), or by adjusting solution conditions (while using the same copolymer). For example, preparing vesicles from copolymers containing polymerizable groups such as poly(methacrylate)44,46,51 or poly(butadiene)61,62 allows for postaggregation cross-linking, which maintains the shape and integrity of the vesicles upon dilution or upon isolation from solution. The chemical nature of the polymer also controls important mechanical properties of the resulting vesicles, such as elasticity and robustness. A recent study reported the formation of “tough” vesicles from poly(ethylene oxide)-b-polyethylethylene block copolymer, with membrane cohesiveness 5-50 larger than that of natural phospholipid-cholesterol membranes.31 Solution properties were also successfully employed to control vesicle size. Studies on polystyrene-b-poly(acrylic acid) vesicles show that vesicles increase in size when the polymer concentration or the water content in the solvent mixture increases.36,58 Vesicle size is also sensitive to the nature (44) Ding, J.; Liu, G. Macromolecules 1997, 30, 655. (45) Ding, J.; Liu, G. Chem. Mater. 1998, 10, 537. (46) Ding, J.; Liu, G. J. Phys. Chem. B 1998, 102, 6107. (47) Holder, S. J.; Sommerdijk, N. A. J. M.; Williams, S. J.; Nolte, R. J. M.; Hiorns, R. C.; Jones, R. G. Chem. Commun. (Cambridge) 1998, 1445. (48) Yu, K.; Bartels, C.; Eisenberg, A. Macromolecules 1998, 31, 9399. (49) Schillen, K.; Bryskhe, K.; Mel’nikova, Y. S. Macromolecules 1999, 32, 6885. (50) Discher, B. M.; Hammer, D. A.; Bates, F. S.; Discher, D. E. Curr. Opin. Colloid Interface Sci. 2000, 5, 125. (51) Nardin, C.; Hirt, T.; Leukel, J.; Meier, W. Langmuir 2000, 16, 1035. (52) Ilhan, F.; Galow, T. H.; Gray, M.; Clavier, G.; Rotello, V. M. J. Am. Chem. Soc. 2000, 122, 5895. (53) Luo, L.; Eisenberg, A. J. Am. Chem. Soc. 2001, 123, 1012. (54) Kukula, H.; Schlaad, H.; Antonietti, M.; Foerster, S. J. Am. Chem. Soc. 2002, 124, 1658. (55) Nardin, C.; Widmer, J.; Winterhalter, M.; Meier, W. Eur. Phys. J. E 2001, 4, 403. (56) Hammer, D. A.; Discher, D. E. Annu. Rev. Mater. Res. 2001, 31, 387. (57) Lee, J. C. M.; Bermudez, H.; Discher, B. M.; Sheehan, M. A.; Won, Y.-Y.; Bates, F. S.; Discher, D. E. Biotechnol. Bioeng. 2001, 73, 135. (58) Luo, L.; Eisenberg, A. Langmuir 2001, 17, 6804. (59) Gravano, S. M.; Borden, M.; von Werne, T.; Doerffler, E. M.; Salazar, G.; Chen, A.; Kisak, E.; Zasadzinski, J. A.; Patten, T. E.; Longo, M. L. Langmuir 2002, 18, 1938. (60) Cornelissen, J. J. L. M.; Fischer, M.; Sommerdijk, N. A. J. M.; Nolte, R. J. M. Science 1998, 280, 1427. (61) Discher, B. M.; Bermudez, H.; Hammer, D. A.; Discher, D. E.; Won, Y.-Y.; Bates, F. S. J. Phys. Chem. B 2002, 106, 2848. (62) Maskos, M.; Harris, J. R. Macromol. Rapid Commun. 2001, 22, 271.
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and composition of the common solvent, the pH, and the ionic strength.63 While several studies investigated properties and potential applications of polymeric vesicles, few addressed questions regarding their thermodynamic nature. Of particular relevance to the present work is a study by Shen et al.,36 which showed that vesicles prepared from polystyrene-b-poly(acrylic acid) in dioxane/water mixtures increase in diameter as the water content in the solvent mixture increases. The increase in size was reversible, suggesting that vesicles are equilibrium structures.36 The thermodynamic nature of vesicles was more thoroughly addressed in a recent study by Luo et al., which showed that vesicles are, in fact, equilibrium structures, stabilized by preferential segregation of the short poly(acrylic acid) chains to the inside of the vesicles, and the long chains to the outside.53 Moreover, it was shown that the change in vesicle size with solvent composition is a thermodynamically controlled process.58 The mechanism for the increase in vesicle size, elucidated using transmission electron microscopy, involves the fusion of vesicles, while the decrease in size occurs by vesicle fission.58 Knowing that vesicles are equilibrium structures that respond to changes in the solvent composition by changing their size, it became of interest to investigate the rate at which these changes occur. Studying the kinetics of vesicle fusion and fission was also motivated by the resemblance of these processes to the numerous membrane fusion and fission events that occur in biological systems.64 Examples include the fusion of myoblasts to form multinucleated muscle cells, and the egg-sperm fusion during fertilization. Also, and within the cell, membrane fusion and fission occur continuously as part of endocytosis, exocytosis, and other transport processes between different intracellular compartments. In biological systems, however, membrane fusion and fission are diverse and rather complex processes that occur at specific times and in response to unique stimuli. The resulting difficulty of performing kinetic measurements in vivo made model membranes, such as liposomes 65-68 and block copolymer vesicles, valuable tools, essential for elucidating the mechanism as well as the kinetics of these events. In the present study, we report on the kinetics of change in vesicle size induced by small perturbations in the solvent composition. Specifically, we evaluate the relaxation times of the increase in vesicle size induced by water addition. Kinetic measurements were performed by monitoring the change in turbidity as a function of time, a method previously used to follow the kinetics of morphological transitions in solution.69-71 We also determine the effect of factors such as the water content in the solvent mixture, the magnitude of perturbation in the solvent composition, the initial polymer concentration, and the acrylic acid block length on the kinetics of vesicle fusion. 2. Experimental Section 2.1. Materials Used. Three samples of polystyrene-b-poly(acrylic acid) block copolymer were used: PS310-b-PAA28, PS310(63) Choucair, A.; et al. To be published. (64) Wilschut, J.; Hoekstra, D. Membrane Fusion; Marcel Dekker: New York, 1991. (65) Lee, J.; Lentz, R. Biochemistry 1997, 36, 6251. (66) Minami, H.; Inoue, T.; Simozawa, R. J. Colloid Interface Sci. 1996, 178, 581. (67) Inoue, T.; Minami, H.; Shimozawa, R.; Sugihara, G. J. Colloid Interface Sci. 1992, 152, 493. (68) Vesicles; Rosoff, M., Ed.; Marcel Dekker: New York, 1996; Vol. 62. (69) Chen, L.; Shen, H.; Eisenberg, A. J. Phys. Chem. B 1999, 103, 9488. (70) Burke, S. E.; Eisenberg, A. Langmuir 2001, 17, 6705. (71) Burke, S. E.; Eisenberg, A. Polymer 2001, 42, 9111.
Fusion of Polystyrene-b-poly(acrylic acid) Vesicles b-PAA36, and PS310-b-PAA45, where the numbers indicate the average degree of polymerization of each block. The samples were synthesized by sequential anionic polymerization, and have a polydispersity of 1.03 as determined by size exclusion chromatography using polystyrene standards. A detailed description of synthesis and characterization procedures is given in previous publications.58,72,73 Dioxane was purchased from Sigma-Aldrich (HPLC grade) and used as received. Deionized water was used in all of the experiments. 2.2. Procedure. 2.2.1. Turbidity Diagrams. The polymer solutions used to construct the turbidity diagrams were prepared in dioxane and had an initial polymer concentration of 0.5% (w/ w). Deionized water was added dropwise to each solution at a rate of 0.2% (w/w) per minute. After the addition of approximately 1% (w/w) of water, the turbidity of the solution was measured. The cycle of water addition and turbidity measurement was continued until the increase in turbidity upon water addition became very small. 2.2.2. Kinetic Measurements. The kinetics of increase in vesicle size were followed by monitoring the turbidity of the solution as a function of time. All turbidity measurements were performed using a Cary 50 UV-visible spectrophotometer, equipped with two silicon diode detectors and a xenon flash lamp. The instrument was set at the absorbance (turbidity) mode, and measurements were recorded every 0.02 min, at λ ) 650 nm. At this wavelength the polymer has minimal absorption, and any attenuation of light is due to scattering from the aggregates. The vesicle solutions were prepared by first dissolving the polymer in dioxane and then adding deionized water dropwise until the concentration required for the formation of vesicles was reached. The solutions were then left to stir overnight to ensure that equilibrium is attained. The initial polymer concentration in all the solutions was 0.5% (w/w), unless mentioned otherwise. A solution of vesicles at a given water content was then placed in a glass cuvette inside the UV-visible spectrophotometer and stirred using an electronic cell stirrer (Starna Spinette, Model scs 1.11). The increase in vesicle size was initiated by adding a given amount of water (corresponding to the desired magnitude of the water jump), and the resulting increase in turbidity was monitored as a function of time. 2.2.3. Transmission Electron Microscopy (TEM). Transmission electron microscopy samples were prepared by adding ca. 30 µL of a polymer solution to an excess of water (resulting in 10-fold dilution) in order to quench the aggregates. A drop of the diluted solution (ca. 10 µL) was then placed on a copper grid, previously coated with a thin film of Formvar and a layer of carbon. The TEM grids were then left to air dry. The morphologies obtained using this method were identical to those obtained using the common temperature-quench/freeze-dry method.36,70 All TEM measurements were carried out on a JEOL JEM-2000 FX electron microscope, operating at an acceleration voltage of 80 keV. The pictures were taken using a multiscan CCD camera. 2.2.4. Electrophoretic Mobility. A microelectrophoresis apparatus (Rank Brothers Ltd., MK II) was used to measure the electrophoretic mobility of vesicle solutions prepared at different water concentrations. All solutions had an initial polymer concentration of 0.25% (w/w) and a water content ranging from 21% to 47% (w/w). The velocity of the aggregates moving under the influence of the applied electric field was evaluated by measuring the time taken by the aggregates to cover a given distance (100 µm in this case). The electrophoretic mobility was then determined using the equation
EM )
velocity of aggregates applied electric field
The electrophoretic mobility, EM, was related to the zeta-potential using the equation74
EM )
2 ζ f(Ka) 3 η
where is the permittivity of the suspending medium, η is its (72) Zhong, X. F.; Varshney, S. K.; Eisenberg, A. Macromolecules 1992, 25, 7160.
Langmuir, Vol. 19, No. 4, 2003 1003 viscosity, ζ is the zeta-potential and f(Ka) is a correction factor whose value is a function of the electric double layer thickness, K-1, and the vesicle radius, a. f(Ka) was estimated from the calculations by O’Brien and White.75 The surface charge density, σ,76 was then determined using the equation77
σ) )
ζ(1 + Ka) a 3 η(1 + Ka) EM 2 af(Ka)
3. Results and Discussion 3.1. Turbidity Diagrams. The block copolymers used in this study undergo a transition from free chains to spheres, to rods, and then to vesicles as the water content in the solvent mixture increases. Therefore, before performing any kinetic measurements, it was important to determine the water concentration at which vesicles exist in solution, and the range over which they are stable. Measuring turbidity as a function of water content is often used to follow the morphological changes of block copolymer aggregates in solution.36,69,70 The transition from rods to vesicles, in particular, is accompanied by a significant increase in turbidity, and therefore is easily determined from turbidity diagrams. Figure 1 shows the turbidity diagrams for solutions of the three block copolymers used: PS310-b-PAA28, PS310-b-PAA36, and PS310-b-PAA45. The increase in turbidity associated with vesicle formation occurs at water concentrations between 12% and 14% (w/w), depending on the acrylic acid block length. To determine the exact water content at which only vesicles exist in solution, (i.e., the endpoint of the rod-vesicle coexistence region), transmission electron microscopy (TEM) was used to identify the morphologies formed at various water contents. In solutions of PS310-b-PAA28, vesicles are present as the only morphology when the water concentration ranges between 14% and 23% (w/w). Below 14%, vesicles coexist with rods, while above 23% they coexist with large compound micelles. For solutions of PS310-b-PAA36, TEM results show that at a water content of 13% (w/w), vesicles still coexist with rodlike aggregates, but are present as the only morphology when the water concentration exceeds 15% (w/w). Finally, for solutions of PS310-b-PAA45, mixtures of rods and vesicles are observed at water concentrations of 15%, 17%, and 18% (w/w), but at concentrations g20% (w/w), only vesicles are present. Based on these results, we concluded that, for PS310-bPAA28 samples, the range for performing kinetic measurements is between a water content of 14% and 23% (w/w), while for PS310-b-PAA36 and PS310-b-PAA45 samples, it starts at 15% and 20% (w/w), respectively, and is limited at the upper end only by the progressively smaller changes in turbidity with water content. Figure 1 also shows that, after vesicle formation, the turbidity of the solution continues to increase with water content, reflecting the increase in vesicle size. The increase in vesicle size can be explained in terms of the effect of the solvent composition on the interfacial energy of the (73) Hautekeer, J. P.; Varshney, S. K.; Fayt, R.; Jacobs, C.; Jerome, R.; Teyssie, P. Macromolecules 1990, 23, 3893. (74) Shaw, D. J. Introduction to Colloid and Surface Chemistry, 4th ed.; Butterworth-Heinemann: Oxford, 1992. (75) O’Brien, R. W.; White, L. R. J. Chem. Soc., Faraday Trans. 2 1978, 74, 1607. (76) The charge density calculated from ζ-potential is the charge at the plane of shear and should not be confused with that at the surface.74 (77) Van de Ven, T. G. M. Colloidal Hydrodynamics; Academic Press: London, 1989.
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Figure 2. Size histogram of vesicles present in a solution of 0.5% (w/w) PS310-b-PAA36 at 25% (w/w) water content.
Figure 1. (a) Turbidity diagrams for solutions of PS310-b-PAA28, PS310-b-PAA36, and PS310-b-PAA45 in dioxane. All solutions have an initial polymer concentration of 0.5% (w/w). (b) Change in vesicle diameter with water content as determined from TEM data for a solution of 0.5% (w/w) PS310-b-PAA36 in dioxane. To guide the eye, we fit the data to a quadratic equation of the form y ) - 0.11x2 + 11.85x - 22.51, with R2 ) 0.989.
system. For polystyrene-b-poly(acrylic acid) vesicles, increasing the water concentration reduces the solvent quality for the polystyrene chains (which form the vesicle wall) and causes an increase in the interfacial tension. In response, and in order to reduce the total interfacial area, vesicle fusion occurs, resulting in an increase in the vesicle size and a decrease in the total number of vesicles.58 The increase in vesicle size with water content for a solution of 0.5% PS310-b-PAA36, as determined from TEM, is shown schematically in Figure 1b. The mechanism of vesicle fusion was elucidated in a previous study using transmission electron microscopy (TEM) and was found to involve several steps.58 First is the collision between two vesicles, followed by adhesion, coalescence, formation of a central wall, destabilization and retraction of the central wall toward the outer wall, and finally smoothing of the outer wall to give a uniform larger vesicle.58 TEM pictures capturing the intermediates involved in the above steps are shown in Figure 8a in ref 58. The pictures of these intermediates were obtained after examining a large number of micrographs since only relatively few intermediate structures were observed at any one time.58 It should be noted that, in principle, fusion is not the only mechanism that could explain the increase in vesicle size with water content. An alternative mechanism, one
that involves the participation of the single chains present in solution, was also considered.58 However, the small value of the cmc (critical micelle concentration) suggests that such a mechanism, although conceivable, is highly improbable. For instance, at water contents of 24%, 29%, 39%, and 50%, which are typical water concentrations at which vesicles are prepared, Luo et al. estimated the fraction of free chains present in solution (relative to total polymer content) to be 10-14, 10-17, 10-24, and 10-32, respectively.58 Thus, the involvement of single chains in the reequilibration of vesicle size is most probably negligible. One wonders, therefore, how the fusion of vesicles can account for small changes in vesicle size occurring in response to small perturbations. For example, if an equilibrated vesicle solution, having an average vesicle diameter of 200 nm, were perturbed to a state where vesicles having an average diameter of 210 nm are the equilibrium structures, how can the fusion of two 200 nm vesicles produce vesicles that are 210 nm in diameter? To clarify how fusion can account for such a situation, it is useful to mention that, at any given water content, the vesicles are polydisperse in size. To illustrate such a polydispersity, we show in Figure 2 the size histogram for vesicles present in a solution of 0.5% w/w PS310-b-PAA36 at a water content of 25% w/w, as determined from TEM pictures. The vesicles in this solution have an average diameter of 202 nm, but the distribution of sizes ranges between 70 and 440 nm with a standard deviation of 75 nm. With such a size distribution, the system can adjust to any new size because the magnitude of the applied perturbation dictates how many vesicles, and of which size, are most likely to fuse, knowing that the fusion does not necessarily involve vesicles of identical size. In addition to the polydispersity effect, fission is also involved in the process through which vesicles equilibrate to new sizes. The same study that discussed the increase in vesicle size via fusion proposed that, in a solution of equilibrated vesicles, fusion and fission occur simultaneously at all times,58 just as in the case of liquid-vapor equilibria, for example, where the molecules are continuously exchanged between the two phases. Therefore, when water is added to a solution of equilibrated vesicles it drives the equilibrium in the direction of fusion, but since the system is dynamic, fission also occurs. Vesicle fission, which is not necessarily symmetrical, contributes to the reequilibration of vesicle size. 3.2. Kinetics of Increase in Vesicle Size. The rate of increase in vesicle size is analyzed according to the
Fusion of Polystyrene-b-poly(acrylic acid) Vesicles
Figure 3. Examples of kinetic measurements for increase in vesicle size in solutions of 0.5% (w/w) PS310-b-PAA36 following successive 5% increases in the water content.
principles of relaxation kinetics. When the equilibrium state of a given system is perturbed, for example by changing the temperature, the pressure, or the concentration, the system responds by adjusting itself to the new set of equilibrium conditions. This adjustment is usually accompanied by a change in the concentration of one or more of the species participating in the equilibrium.78 The time required for self-adjustment to occur, or the rate at which the system relaxes toward its new equilibrium, is related to the kinetics of the reaction involved, and is thus the quantity of interest in relaxation kinetics measurements. In a typical experiment, the equilibrium of a system is perturbed, and using a suitable detection method, the change in concentration or, more commonly, the change in a physical property proportional to concentration is monitored as a function of time.78,79 This method is often used to measure the kinetics of morphological transitions of block copolymer69-71,80 and surfactant aggregates.81-83 In the present system, the equilibrium of a solution of vesicles of a given size is perturbed by adding water. To adjust to the new solvent composition, the vesicle size increases, causing an increase in the turbidity of the solution. The kinetics of vesicle fusion is thus followed by monitoring the change in turbidity as a function of time. Figure 3 shows examples of kinetic measurements for solutions of 0.5% (w/w) PS310-b-PAA36. The increase in turbidity occurs after the successive addition of 5% (w/w) of water. The turbidity curves best fit a single-exponential function of the form
∆T ) A(1 - exp (-t/τ)) where ∆T is the change in turbidity over time t (relative to its value before water addition), τ is the relaxation time, and A is an adjustable parameter. As mentioned earlier, vesicle fusion is a multistep process, and is therefore (78) Bernasconi, C. F. Relaxation Kinetics; Academic Press: New York, 1976. (79) Laidler, K. J. Chemical Kinetics, 2nd ed.; McGraw-Hill Inc.: New York, 1965. (80) Iyama, K.; Nose, T. Macromolecules 1998, 31, 7356. (81) Robinson, B. H.; Bucak, S.; Fontana, A. Langmuir 2000, 16, 8231. (82) Farquhar, K. D.; Misran, M.; Robinson, B. H.; Steytler, D. C.; Morini, P.; Garrett, P. R.; Holzwarth, J. F. J. Phys.: Condens. Matter 1996, 8, 9397. (83) O’Connor, A. J.; Hatton, T. A.; Bose, A. Langmuir 1997, 13, 6931.
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characterized by more than one relaxation time. However, to observe several relaxation times experimentally, a number of conditions should be satisfied.78 First, the intermediate states should accumulate to detectable concentrations. Second, the different relaxation times should be strongly separated. If two or more relaxation times are identical, or very similar in value, it becomes very difficult to distinguish between them experimentally, leading to a reduction in the number of observable relaxation times. Finally, the detection method should be able to distinguish between the different intermediates. Among the three different conditions, we believe that at least the third is difficult to achieve in the present system. The first step in the process of vesicle fusion involves the adhesive collision between two vesicles and the formation of the first intermediate: a vesicle doublet. During the subsequent steps, structural changes occur in small increments, resulting in intermediates that differ only slightly in shape. Consequently, the change in the amount of light scattered (i.e., the change in the turbidity signal) accompanying the formation of each intermediate is small, and is thus difficult to distinguish from the noise signal. 3.2.1. Effect of Water Content. The composition of the dioxane/water solvent mixture affects the rate of increase in vesicle size. To examine this effect, we added the same percentage of water (i.e., the same magnitude of perturbation) to solutions having different water contents and measured the resulting increase in turbidity as a function of time. Figure 3 shows the effect of solvent composition on the kinetics. The curves correspond to four solutions having initial water concentrations of 15%, 20%, 25%, and 30% (w/w), respectively. Although the same percent of water was added to the four solutions (5% w/w), the resulting increase in turbidity (∆T) decreases as the water content increases. This observation indicates that larger changes in vesicle size occur at lower water concentrations. To follow these changes, we used TEM to determine the size of vesicles present in the four solutions, before and after water addition. The results show that as the water content increases from 15% to 20%, 25%, 30%, and 35% (w/w), the vesicle size increases progressively from (diameter ( standard deviation) 125 ( 42 nm, to 167 ( 49, 202 ( 74, 240 ( 108, and 256 ( 103 nm, respectively (Figure 1b). These values reflect a decrease in the percent change in vesicle size from 34% to 22%, 18%, and 7%, respectively, which explains the observed decrease in turbidity change (∆T) with water content. Figure 3 also shows that as the water content in the solvent mixture increases, the increase in vesicle size occurs over longer periods of time, (indicated by the increase in the value of the relaxation times from 11 to 18, 20, and 34 s). In fact, the increase in relaxation times with water content is a general trend observed even when different magnitudes of perturbation were applied (section 3.2.2), or when different polymer concentrations were used (section 3.2.3), and was common to vesicles prepared from the three different block copolymers (section 3.2.4). This trend can be explained in terms of the effect of solvent composition on two factors: the chain dynamics within vesicles and the vesicle collision rate. When polystyrene-b-poly(acrylic acid) vesicles are prepared in dioxane/water mixtures, the polystyrene wall is swelled with dioxane, which is a better solvent for polystyrene than water. This can be seen from the values of the solubility parameters of polystyrene, dioxane, and water, which are δPS ) 8.1-9.9, δdioxane ) 10.0, and
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Table 1. Increase in Electrophoretic Mobility, EM, and Surface Charge Density, σ, with Water Content for Solutions of 0.25% (w/w) PS310-b-PAA36 water % (w/w) EM/10-9 (m2/V‚s) σ/10-3 (C/m2)
21 3.1 ( 0.3 1.2 ( 0.1
25 4.0 ( 0.4 1.4 ( 0.1
δwater ) 23.4 [cal/cm3]1/2, respectively.84 As the water concentration in solution increases, the dioxane content in the polystyrene walls decreases.40 (For example, the dioxane content in swelled homopolystyrene decreases from ca. 75% v/v to 40% v/v when the water content increases from 10% to 17% w/w40). Consequently, the degree of swelling of the polystyrene chains is reduced and the viscosity of the vesicle wall increases. With the resulting decrease in chain mobility, longer times become required for the chains to rearrange during the several steps of vesicle fusion. In addition to its effect on chain dynamics, the water content changes the rate of collision between vesicles by influencing three factors: the collision efficiency, the number of vesicles present in solution (i.e., the number of colliding aggregates per unit volume), and the vesicle size. Since water has a higher dielectric constant than dioxane (water ) 78.5 and dioxane ) 2.2),85 increasing the water content in the solvent mixture leads to an increase in the degree of ionization of the acrylic acid chains, and thus to an increase in the vesicle surface charge density. The resulting increase in the electrostatic repulsion between colliding vesicles reduces the collision efficiency (i.e., the number of “sticky” collisions per unit time). The increase in the vesicle surface charge density with water content was followed by measuring the electrophoretic mobility. The results, summarized in Table 1, show that the electrophoretic mobility increases from 3.1 to 7 m2/ V‚s, and the surface charge density increases from 1.2 × 10-3 to 2.0 × 10-3 C/m2, as the water content increases from 21% to 47% (w/w). Details of the calculations are given in the Supporting Information. In addition to stronger electrostatic repulsion, the increase in the degree of ionization of acrylic acid enhances the steric repulsion as well. When the chains become more negatively charged, they are forced to extend away from the vesicle surface and into the solution. With a larger corona brush thickness, the steric repulsion between two approaching vesicles increases, further reducing the collision efficiency.7 Another factor that contributes to the decrease in the collision rate with water content is the decrease in the vesicle concentration (i.e., the number of vesicles per unit volume). Since water addition induces vesicle fusion, the total number of vesicles per unit volume decreases as the water content in the solvent mixture increases. The calculated drop in vesicle concentration with vesicle diameter is shown in Figure 4. Details of the calculations are given in the Supporting Information. For example, in a 0.5% polymer solution, and at a water content of 15%, the vesicle diameter is ca. 125 nm and the calculated vesicle concentration is ca. 5.4 × 1012 vesicles/mL, while at a water content of 25% the vesicle diameter is ca. 202 nm and the vesicle concentration is ca. 1.7 × 1012 vesicles/mL. It is important to note that the increase in vesicle size with water content opposes the effect of lower collision efficiency and smaller vesicle concentration and contributes to an increase in the rate of vesicle collision. However, the observed increase in the average relaxation times with water content suggests that the decrease in the collision (84) Brandrup, J.; Immergut, E. H. Polymer Handbook, 3rd ed.; John Wiley and Sons: New York, 1989. (85) Weast, R. C. Handbook of Chemistry and Physics, 60th ed.; CRC Press: Boca Raton, FL, 1979-1980.
29 5.1 ( 0.7 1.6 ( 0.2
35 5.4 ( 0.4 1.8 ( 0.3
41 6.2 ( 0.5 1.9 ( 0.2
47 7(2 2.0 ( 0.5
Figure 4. Calculated decrease in vesicle concentration with vesicle size for two block copolymer concentrations. The y-axis has a logarithmic scale.
Figure 5. Effect of percent of water added on relaxation times for solutions of 0.5% (w/w) PS310-b-PAA36.
efficiency and vesicle concentration, as well as the slower chain dynamics, dominate the effect of larger vesicle size and account for the decrease in fusion rates. 3.2.2. Effect of Magnitude of Perturbation. To examine the effect of the magnitude of perturbation on the kinetics, we evaluated the relaxation times for an increase in vesicle size induced by the addition of different percentages of water. The sizes of water jumps used were 1%, 2%, and 5% (w/w). Perturbations smaller than 1% (w/w) induced changes in the turbidity that were too small to follow without introducing significant experimental error. On the other hand, addition of more than 5% (w/w) of water resulted in kinetically arrested morphologies. Figure 5 summarizes the results obtained for solutions of PS310b-PAA36 with an initial polymer concentration of 0.5% (w/w). For a given magnitude of perturbation, the average relaxation time increases with water content, in accordance with the general trend discussed before. Figure 5 also shows that the higher the extent of perturbation, the lower is the value of the relaxation time, or the faster are the relaxation kinetics. To illustrate how larger perturbations result in shorter relaxation times, it is useful to express the value of τ in terms of the vesicle concentration. The fusion between two vesicles to produce a larger
Fusion of Polystyrene-b-poly(acrylic acid) Vesicles
Langmuir, Vol. 19, No. 4, 2003 1007 Table 2. Effect of Initial Polymer Concentration on Vesicle Size and Vesicle Concentration for Solutions of PS310-b-PAA36 polymer concentration (w/w) 0.25%
Figure 6. Effect of polymer concentration on relaxation times for solutions of PS310-b-PAA36 at concentrations of 0.25% (b) and 0.5% w/w (2).
one may be represented by the equation86 k1
A + B {\ }C k -1
where A and B are the fusing vesicles (which are not necessarily of the same size) and C is the resulting larger vesicle. k1 and k-1 represent the rate constants for the forward and backward reaction, respectively. The inverse relaxation time for such a reaction can be expressed as (the complete derivation of the following equation is shown in the Supporting Information)
[A]f[B]f 1 ) k-1 - k1 τ [C]0
water % (w/w)
diam (nm)
vesicle concn/ 1012 (vesicles/mL)
diam (nm)
vesicle concn/ 1012 (vesicles/mL)
17 20 25
114 ( 23 123 ( 21 131 ( 10
3.4 2.8 2.5
158 ( 43 167 ( 49 204 ( 80
3.1 2.6 1.7
content. However, for a given increase in the water content, shorter relaxation times were observed for the more concentrated solutions, indicating that an increase in the initial polymer concentration results in faster rates. The effect of the initial polymer concentration on the kinetics can be explained in terms of its effect on vesicle size and vesicle concentration, which, in turn, influence the rate of vesicle collision. In the process of vesicle fusion, the first step involves the collision between two vesicles and the formation of a vesicle doublet.58 The rate at which doublets are formed is a function of both the Brownian motion of the aggregates and the shear rate.77 In the present system, small shear rates were applied (G ≈ 5 s-1) and the value of the Peclet number, Pe, ranged between 0.004 and 0.05. (Pe ) Ga2/D, where G is the shear rate, a is the vesicle radius, and D is the diffusion coefficient.) Under these conditions the rate of doublet formation can be expressed as77
ratedoublet ) J0(1 + 0.5136RpPe1/2 + ...)
(86) It is important to note that we are using this equation as an illustration, and we are not reporting any information about the order of the reaction. In fact, as far as the reaction order is concerned, the only definitive information that can be extracted from this study is that the reaction is not first order. In first-order reactions, the relaxation time is independent of concentration, while for the fusion process, the evaluated relaxation times were concentration dependent. (87) For the PS310-b-PAA36 samples, we considered solutions prepared at initial polymer concentrations of 0.25%, 0.5%, 1.0%, and 2.0% (w/w). However, in solutions at 1.0% and 2.0% (w/w), vesicles existed only over a narrow region of water contents; therefore, these solutions were not used for kinetic measurements.
(2)
where J0 is the flux due to diffusion of aggregates and Rp is the collision efficiency. Knowing that
(1)
where [A]f and [B]f are the concentrations of the fusing vesicles at the end of the relaxation process and [C]0 is the initial concentration of the large vesicles. Starting from any given water content, and as the magnitude of perturbation increases, the final concentrations of the reacting vesicles, [A]f and [B]f, decrease. This is because with the addition of more water, larger vesicles are produced at the expense of the smaller ones. According to eq 1, smaller values of [A]f and [B]f result in larger values of 1/τ, or shorter relaxation times. 3.2.3. Effect of Polymer Concentration. The initial polymer concentration is another factor that influences the kinetics of increase in vesicle size. This effect is examined by adding the same water percentage to vesicle solutions prepared at different polymer concentrations, and comparing the obtained relaxation times. Figure 6 shows the results for two solutions of PS310-b-PAA36 prepared at an initial polymer concentration of 0.25% and 0.5% (w/w).87 The increase in vesicle size was induced by a 2% (w/w) jump in the water concentration. For both solutions, the average relaxation times increase with water
0.50%
J0 ) 16πRpnaD and
D ) KT/6πηa where n is the vesicle concentration (i.e., the number of vesicles per unit volume), η is the viscosity of the suspending medium, K is the Boltzmann constant, and T is the temperature in kelvin, eq 2 can be written as
ratedoublet ) 1.1 × 10-17Rpn(1 + 0.5136RpPe1/2 + ...) (3) According to eq 3, the rate of doublet formation is a function of the vesicle concentration, n, the vesicle size (through the value of the Peclet number, Pe), and the collision efficiency, Rp, all of which are sensitive to changes in the initial polymer concentration. TEM results show that, at a given water content, vesicles increase in size by increasing the polymer concentration (Table 2). With bigger aggregates, the radius of the collision sphere is larger and the collision efficiency (i.e., the number of captures per unit time) increases.77 The vesicle wall thickness, on the other hand, does not increase with polymer concentration, meaning that while bigger vesicles are formed, the number of vesicles per unit volume decreases. Based on the diameter and the wall thickness determined from TEM, we estimated the change in vesicle concentration with polymer concentration. The results summarized in Table 2 show that with the increase in the polymer concentration from 0.25% to 0.5% w/w, the decrease in vesicle concentration ranges from 9% to 32%, depending on the water content. The increase in vesicle
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Figure 7. Effect of poly(acrylic acid) block length on relaxation times. All the solutions have an initial polymer concentration of 0.5% (w/w).
Eisenberg and Choucair
respectively (representative TEM pictures of these solutions are shown in Figure 8). The calculated vesicle concentration in these solutions corresponds to 7.5 × 1012, 2.6 × 1012 (66% decrease), and 0.3 × 1012 vesicles/mL (88% decrease), respectively. The decrease in vesicle concentration leads to slower collision rates, while the increase in vesicle size (and the accompanying increase in the capture efficiency) causes an increase in the rates. Experimentally, we observed a slight decrease in the fusion rates accompanying a decrease in the PAA block length, showing that the drop in vesicle concentration compensates for the effect of larger vesicle size. 3.3. Kinetics of Decrease in Vesicle Size. An attempt was also made to examine the kinetics of decrease in vesicle size. Different percentages of dioxane were added to vesicle solutions to induce the decrease, but the resulting change in turbidity occurred rapidly (less than 10 s), so that information about the relaxation time could not be obtained using this technique. Kinetic measurements using the stopped-flow technique will be the subject of a subsequent paper. 4. Conclusion
Figure 8. TEM pictures of vesicles present in solutions of (A) PS310-b-PAA28, (B) PS310-b-PAA36, and (C) PS310-b-PAA45. All solutions have an initial polymer concentration of 0.5% (w/w) and a water content of 20% (w/w).
size and collision efficiency on one hand, and the decrease in the vesicle concentration on the other hand have opposing effects on the rate of doublet formation. Experimentally, we observed that an increase in the polymer concentration results in faster rates, suggesting that the effect of the first two factors compensates for the decrease in vesicle concentration. 3.2.4. Effect of Poly(acrylic acid) Block Length. To examine the effect of poly(acrylic acid) block length on the rate of vesicle fusion, kinetic measurements were performed on vesicles prepared from three block copolymers with the same polystyrene block length, but with varying poly(acrylic acid) blocks. Figure 7 summarizes the results obtained when the same magnitude of perturbation (2% w/w jump in the water content) was applied to vesicle solutions of the three block copolymers (all having a polymer concentration of 0.5% w/w). The results show that as the PAA block length decreases, vesicle fusion occurs at slower rates. The effect of PAA block length on kinetics of vesicle fusion reflects, once again, the effect of vesicle size and vesicle concentration on the rate of vesicle collision. Determining the size of vesicles prepared from the three block copolymers using TEM showed that, at a given water content and polymer concentration, block copolymers of shorter PAA blocks form larger vesicles (Figure 8). However, the polystyrene wall thickness does not change, meaning that while block copolymers with shorter PAA blocks form larger vesicles, the total number of vesicles per unit volume is smaller. For example, at a water concentration of 20% (w/w), vesicles prepared in 0.5% w/w solutions of polystyrene310-b-poly(acrylic acid)45, polystyrene310-b-poly(acrylic acid)36, and polystyrene310-b-poly(acrylic acid)28 are 110, 170, and 440 nm in diameter,
Vesicles of polystyrene-b-poly(acrylic acid) prepared in dioxane-water mixtures are equilibrium structures that increase in size when the water content in the solvent mixture increases. The mechanism for this increase, elucidated using TEM, involves vesicle fusion.58 In this paper we have discussed the kinetics of increase in vesicle size induced by water addition. Kinetic measurements were performed by monitoring the change in turbidity as a function of time following an increase in the water concentration. The average relaxation times, evaluated from the turbidity curves, range in value between 10 and 700 s, depending on parameters such as the water content in the solvent mixture, the magnitude of perturbation, the polymer concentration, and the poly(acrylic acid) block length. Vesicle fusion occurred at progressively slower rates as the water content in the solvent mixture increased. The slower rates are attributed to the decrease in both the chain mobility and the vesicle collision frequency with increasing water content. On the other hand, increasing the magnitude of perturbation resulted in faster rates. The effect of polymer concentration and poly(acrylic acid) block length on relaxation times reflected the effect of these variables on vesicle size and vesicle concentration (i.e., number of vesicles per unit volume). By increasing the polymer concentration, larger vesicles are formed, while the total number of vesicles decreases slightly. The net effect is faster fusion rates. On the other hand, a decrease in the poly(acrylic acid) block length from 45 to 36 and to 28 units results in the formation of bigger vesicles as well, but the decrease in the vesicle concentration is larger compared to the one accompanying an increase in the polymer concentration, and the result of a decrease in poly(acrylic acid) block length is a slight decrease in the relaxation rates, indicated by the small increase in the average relaxation times. Acknowledgment. We thank Dr D. Ronis and Dr. T. G. M. Van de Ven for valuable discussions, as well as the National Science and Engineering Research Council (NSERC) for financial support. Supporting Information Available: Details for evaluating the surface charge density, the vesicle concentration, and the equation of the average relaxation time. This material is available free of charge via the Internet at http://pubs.acs.org. LA026187K
