Sol−Gel Transition Temperature of PLGA-g-PEG Aqueous Solutions

Biomacromolecules 2002, 3, 511-516

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Sol-Gel Transition Temperature of PLGA-g-PEG Aqueous Solutions Young-Me Chung, Kevin L. Simmons, Anna Gutowska, and Byeongmoon Jeong* Pacific Northwest National Laboratory (PNNL), 902 Battelle Boulevard, P.O. Box 999, K2-44, Richland, Washington 99352 Received November 15, 2001; Revised Manuscript Received February 8, 2002

Aqueous solutions of poly(DL-lactic acid-co-glycolic acid)-g-poly(ethylene glycol) copolymers exhibited sol-to-gel transition with increasing temperature. Further increase in temperature makes the system flow and form a sol phase again. Subcutaneous injection of a copolymer aqueous solution (0.5 mL) resulted in a formation of a hydrogel depot by temperature-sensitive sol-to-gel transition in a rat model. The reliable determination and control of sol-to-gel transition temperatures are the most important issues for this kind of sol-gel reversible hydrogel. The sol-to-gel transition temperature determined by the test tube inverting method, falling ball method, and dynamic mechanical analysis coincided within 1-2 °C. Fine tuning of the sol-to-gel transition temperature was achieved by varying the ionic strength of the polymer solutions and by mixing two polymer aqueous solutions with different sol-to-gel transition temperatures. The sol-to-gel transition temperature of polymer mixture aqueous solutions was well described by an empirical equation of miscible blends, indicating miscibility of the two polymer systems in water on the molecular level. Introduction Self-assembly of polymers by external stimuli has been studied extensively in the past decade.1-3 Thermoreversible polymers that can form a gel in situ are especially attractive as injectable implant systems for sustained drug delivery and tissue engineering. N-Isopropyl acryl amide copolymers, poloxamers, poly(acrylic acid)-g-poloxamers, chitosanglycerol phosphate, poly(ethylene glycol)/poly(DL-lactic acidco-glycolic acid) triblock/graft copolymers, and poly(ethylene glycol)/poly(propyl fumarate) block copolymers are typical systems exhibiting the sol-to-gel transition in water as the temperature increases.4-10 To achieve an ideal injectable system, the polymer aqueous solution should flow freely at room temperature and form a gel at body temperature. In addition, kinetics of the sol-togel transition should be fast as it is related to the initial burst of the incorporated drug, the shape of gel depot, and, consequently, the drug release profile. The determination and control of the sol-to-gel transition temperature in a reliable manner are quite important because the sol-to-gel transition temperature determines injectability, formulation temperature, and sterilization condition. Because sol-to-gel transition is driven by thermal conduction, the solto-gel transition is faster when the transition temperature is much lower than 37 °C. Thus, the kinetics of gel formation is determined by sol-to-gel transition temperature. Faster gelation means a lower initial burst of pharmaceutical agents. Traditionally, a simple test tube inverting method has been used for determination of the sol-gel transition tempera* To whom correspondence should be addressed. Current address: Department of Chemistry, Ewha Womans University, Seoul, Korea. Tel: 82-2-3277-3411. Fax: 82-2-3277-2384. E-mail: [email protected].

tures.11,12 The falling ball method is also used to determine the sol-gel transition temperature. It measures the amount of time that a ball of a specific weight travels a fixed distance through the sol or gel phase.13 Dynamic mechanical analysis can be used for the determination of the sol-gel transition temperature.7,14 This method allows study of the microphase separation of a material.15 For polymer mixtures with microphase separation, two transitions corresponding to each polymer are observed. When two polymers are miscible, the mixture shows one transition at the midpoint of the two transition temperatures of each polymer. Mixing of fully miscible polymers exhibiting two different transitions can be used as a simple method to control the sol-to-gel transition temperature of a polymer aqueous solution. Aiming at design of an optimal injectable polymer formulation based on poly(DL-lactic acid-co-glycolic acid)g-poly(ethylene glycol) (PLGA-g-PEG) copolymer, we investigated the in vivo gel formation after subcutaneous injection in a rat model. We also compared several methods for determining the sol-to-gel transition of PLGA-g-PEG polymer aqueous solutions to test the reliability of each method. Finally, we studied change in the sol-to-gel transition by varying the ionic strength of phosphate buffer saline (PBS) and by mixing two PLGA-g-PEG polymer aqueous solutions with different sol-to-gel transition temperatures. Materials and Methods Materials. Epoxy-terminated poly(ethylene glycol) (EPEG) (molecular weight 600 and 1000; Shearwaters Polymers Inc.), monomethoxy-terminated PEG (MPEG) (molecular weight 550 and 1000; Aldrich), and glycolide (Polyscience) were used as received. DL-Lactide (Polyscience) was recrystallized

10.1021/bm0156431 CCC: $22.00 © 2002 American Chemical Society Published on Web 03/29/2002

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Table 1. Lists of the PLGA-g-PEG Polymer PLGA-g-PEG copolymer

(Mn)a

PDIa,b

compositionc (DDLA/GA/EG)

no. of PEG grafts per PLGA backboned (z)

I II III

9000 6000 10000

1.8 1.7 2.0

3.17/1.0/2.62 3.28/1.0/2.71 3.13/1.0/3.99

4 3 4

lines of travel time of the steel ball. A dynamic viscosity (µ) can be calculated using the specific weight of the sphere (γs), the specific weight of the fluid (γf), the diameter of the sphere (D), and the velocity of the sphere (V) by following eq 1.17 µ ) (γs - γf)D2/(18V)

(1)

a

Number average molecular weight determined by gel permeation chromatography. b Polydispersity index. c Determined by 1H NMR of PLGA-g-PEG copolymers in CDCl3 based on ethylene glycol (4H, 3.6 ppm), lactic acid (3H, 1.5 ppm), and glycolic acid (2H, 4.8 ppm) moieties of the polymers. d Number of graft (z) was calculated from molecular weight and composition based on PEG molecular weight.The contribution from connecting groups and end groups to Mn is less than 500 and can be ignored. As the first-order approximation, Mn and z are given by the following equations: Mn ∼ 72x + 58y + 44z′; z ∼ 44z′/600 for I, II; z ∼ 44z′/1000 for III; z′ ∼ zm (where x, y, z′, z, and m are the number of repeating units of lactic acid, glycolic acid, ethylene glycol, number of PEG grafts per PLGA backbone, and number of repeating units in each PEG graft, respectively, and the mole ratio of x/y/z′ is given the fourth column of the table.

Figure 1. Chemical structure of a PLGA-g-PEG copolymer.

from ethyl acetate. The PLGA-g-PEG copolymer was prepared by one-step ring opening polymerization of glycolide, DL-lactide, and EPEG using stannous octoate as a catalyst.16 For example, to prepare polymer I (Table 1), the toluene solution (220 mL) of MPEG (2.5 g, molecular weight 550) and EPEG (25 g) was azeotropically distilled to a final volume of 50 mL to remove residual water. DL-Lactide (28 g) and glycolide (7 g) were added to the MPEG/EPEG toluene solution. After the dissolution of the DL-lactide and glycolide, stannous octoate (400 µL) was added and the mixture was stirred for 24 h at 120 °C. The polymerized mixture was diluted with methylene chloride and then precipitated into ethyl ether. The chemical structure is shown in Figure 1. Table 1 describes lists of the PLGA-g-PEG copolymers used in this study. Nuclear Magnetic Resonance (NMR). An NMR spectrometer (Varian VXR 300) was used to study composition (1H NMR in chloroform-d (CDCl3)) and microenvironment (13C NMR in deuterium oxide (D2O)) of PLGA-g-PEG copolymers. For the 13C NMR in D2O, a 25 wt % PLGAg-PEG solution was prepared. Test Tube Inverting Method. A series of PLGA-g-PEG (I) aqueous solutions, 23, 25, 27, 29, and 31 wt %, were prepared. A 0.5 mL portion of the solution was put in a 4 mL vial with a diameter of 1.0 cm. The sol-gel transition temperature was determined by flow or no-flow criterion over 30 s with the test tube inverted. The temperature was controlled at the heating rate of 0.2 °C/min, and the transition temperature was monitored at an accuracy of (1 °C. Falling Ball Method. With this method, 2.0 mL of PLGAg-PEG (I) polymer solution and a steel ball (diameter ) 2.2 mm, density (Fs) ) 7.6 g/mL) were put in the NMR tube with a diameter of 4.2 mm. The time period for the steel ball to fall 5 cm was measured. The sol-to-gel transition temperature is defined by the intersection of extrapolated

where γs ) Fsg, γf ) Ffg, and V ) travel distance/travel time. g is a gravitational acceleration of 980 cm/s2, and Ff is the density of the fluid. Dynamic Mechanical Analysis. The sol-gel transition of the PLGA-g-PEG copolymer aqueous solution was investigated using dynamic rheometry (Rheometric Scientific, SR 2000). The polymer solution was placed between parallel plates of 25 mm diameter and a gap of 0.5 mm. The data were collected under a controlled stress (4.0 dyn/cm2) and a frequency of 1.0 rad/s. The heating and cooling rates were 0.2 °C/min. For comparison, the sol-to-gel transition at different heating rates of 0.2, 0.5, and 1.0 °C/min at a fixed frequency of 1.0 rad/s were studied. The sol-to-gel transition at different frequencies of 0.5, 1.0, and 3.0 rad/s at a fixed heating rate of 0.2 °C/min were also studied. In Vivo Gel Depot. To test in vivo gel depot formation, 0.5 mL of PLGA-g-PEG (I) polymer aqueous solution (29 wt. %) was injected subcutaneously using a syringe with 22gauge needle after anesthetizing the rat with carbon dioxide. One week after the injection, the injection site was cut open and the in situ formed gel was investigated. Control of Sol-to-Gel Transition. First, phosphate buffer saline (PBS) solutions with different ionic strengths ranging from 0 to 120 mM were prepared and the sol-to-gel transition temperatures of 25 wt % polymer (I) solutions were investigated. Second, two polymer (II and III) aqueous solutions (29 wt %) with different sol-to-gel transition temperatures were selected. The sol-to-gel transition temperatures were studied by the dynamic mechanical analysis of polymer mixtures with different ratios of polymer II and III. Dye Solubilization. The concentration of the hydrophobic dye, 1,6-diphenyl-1,3,5-hexatriene, was fixed at 4 µM, while the PLGA-g-PEG copolymer concentration varied from 0.01 to 0.25 wt %. The UV-vis spectra (HP 8453) were recorded in the range of 280-600 nm at 20 °C. Results and Discussion The aqueous solution of PLGA-g-PEG is a free-flowing sol at room temperature or lower and becomes a gel about 25-30 °C depending on the polymer concentration. The gel phase persists to about 45 °C and flows again by gel-to-sol transition above 45 °C. The phase diagram determined by the classical test tube inverting method is shown in Figure 2. The gel phase observed at about 37 °C indicates its potential as an in situ gel forming biomaterial. The applicability of this material as an in situ gel forming device was tested by subcutaneous injection of a 0.5 mL aqueous polymer solution (29 wt %) into the rat. The gel was round shaped rather than spread sheet shaped, indicating

Sol-Gel Transition Temperatures

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Figure 2. The phase diagram of PLGA-g-PEG copolymer (I) aqueous solution. Sol-gel transition temperatures were determined by the test tube inverting method. Black squares are sol-to-gel transition temperatures, and gray squares are gel-to-sol transition temperatures.

Figure 3. In situ gel formation of a PLGA-g-PEG aqueous solution (29 wt %). A 0.5 mL portion of PLGA-g-PEG (I) polymer aqueous solution was subcutaneously injected into the rat. Photo taken 1 week after the injection shows a gel depot.

fast gelation kinetics for in vivo application (Figure 3). Interestingly, the PLGA-g-PEG gel depot persisted more than 2 months in vivo whereas the gel depot of PEG-g-PLGA that has a hydrophilic PEG backbone was absorbed within a week. The fast absorption of the in situ formed gel might have been caused by a relatively weak mechanical property of the gel resulting from the flexible PEG backbone and the inherent small segments of PLGA diffusing easily out of the gel depot. Considering the fact the duration of a depot is important in delivery system design, the control of gel duration by a simple topological change of polymer structure from hydrophilic backbone-hydrophobic grafts to hydrophobic backbone-hydrophilic grafts is an interesting finding. The sol-to-gel transition temperature is the most fundamental parameter in the sol-gel reversible hydrogel as discussed in the previous section. Therefore, the reliable method to determine the sol-to-gel transition is a critical issue. The criterion of flow (sol)-no flow (gel) criteria in test tube inverting method is rather subjective but is the simplest method to determine the sol-to-gel transition. Multiple samples can be measured at a time by the test tube inverting method. Due to its simplicity and efficiency, this method has been widely used. In the falling ball method, the measurement of a falling ball of a known diameter and density falls through a fluid under the influence of gravity. The ball will accelerate downward under its weight until it is balanced by a buoyant force and viscosity drag force acting upward on it. The experiment measured the time for a steel ball to fall 5 cm due to gravitational force. The steel ball rapidly dropped

Figure 4. Determination of sol-to-gel transition temperature of PLGAg-PEG copolymer (I) aqueous solution (29 wt %) by extrapolation of two lines from a curve describing the falling time of steel ball over 5 cm as a function of temperature. The abrupt increases of travel time (a) and dynamic viscosity (b) are caused by sol-to-gel transition of the polymer solution. The dynamic viscosity was calculated by eq 1 assuming the density fluid (∼1.0 g/cm3) is not changed during solto-gel transition.

through the sol phase with little resistance, whereas it is very difficult for the ball to travel through the gel phase. The extrapolation of the two lines in a time versus temperature plot provided an intersection. This point was used for the determination of the sol-to-gel transition temperature (Figure 4a). The corresponding dynamic viscosity changes calculated by eq 1 as a function of temperature are shown in Figure 4b. The volume change during the sol-to-gel transition was measured as less than 5%; therefore, the density of sol and gel was assumed to be 1.0 g/cm3 in the calculation. A vertical curve over 25-27 °C in this plot indicates the sensitivity of the thermogelling transition. The falling ball method provides more reliable data by extrapolating the time curve to temperature axis, compared with the flow or no-flow decision of a test tube inverting method. The dynamic mechanical analysis shows storage modulus (G′) and loss modulus (G′′) at the same time. Storage modulus is a measure of the load-bearing capacity and loss modulus comes from the viscous component of a material when a cyclic deformation is applied. Therefore, we can see the sol-to-gel transition by following G′ or G′′ increases. Figure 5 shows the change in storage modulus of PLGA-gPEG copolymer aqueous solutions. As the temperature monotonically increases, the storage modulus increases at the sol-to-gel transition temperature. The abrupt change in storage modulus can be used as a criterion for the determination of the sol-to-gel transition. As the polymer concentration increased, the sol-to-gel transition temperature decreased, due to an increase in the available physical cross-linking points that are dependent on the polymer concentration. The presence of a gel phase at 37 °C over 23-31 wt % of PLGAg-PEG polymer aqueous solutions indicates promising bio-

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Figure 5. Storage modulus (G′) of PEG-g-PLGA (I) aqueous solutions as a function of temperature. G′ was measured as the temperature increases at a heating rate of 0.2 °C/min at oscillating frequency of 1.0 rad/s. The legends are polymer concentration in water. In sol state, G′ is negligibly small and was not recorded. Around 25 °C, G′ increases abruptly, indicating sol-to-gel transition.

Figure 6. Comparison of the sol-to-gel transition temperature determined by the test tube inverting method (TIM), the falling ball method (FBM), and dynamic mechanical analysis (DMA). Heating rate was fixed at 0.2 °C/min for all experiments, and oscillating frequency in DMA was 1.0 rad/s.

material for injectable depot systems for drug delivery and tissue engineering. When different heating rates of 0.2, 0.5, and 1 °C/min were compared, the transition temperature of PLGA-g-PEG copolymer aqueous solution (29 wt %) was practically unchanged, indicating enough thermal equilibrium in these heating rates. When the frequencies of oscillatory stress increased from 0.5 to 3 rad/s, the transition temperature of PLGA-g-PEG copolymer aqueous solution (29 wt %) was increased by 1-2 °C. It would be helpful to have stronger intermolecular forces to form a tight gel against the mechanical shear stress that might hamper the gel formation in this experimental time scale. However, the gel modulus increases as the frequencies increase, which is the typical behavior of thermoplastics with shear thickening effects. To summarize, the sol-gel transition temperatures determined by the test tube inverting method, the falling ball method, and dynamic mechanical analysis are plotted in Figure 6. An agreement of the sol-to-gel temperatures within 1-2 °C indicates that all of the previous methods are proper candidates for the determination of the sol-gel transition. Dynamic mechanical analysis gives the behavior of materials modulus, important for biomedical applications where the optimal mechanical stress should be known. This study also addresses the validity of the test tube inverting method, the most widely used method to develop a sol-gel phase diagram. The effect of ionic strength was also investigated to fine tune the sol-to-gel transition temperature of PLGA-g-PEG aqueous solutions. Basically, all intermolecular forces, such

Chung et al.

Figure 7. Sol-gel transition temperature of PLGA-g-PEG aqueous solutions (25 wt %) by changing ionic strength of PBS. The legends are ionic strength of PBS that varied from 0 to 120 mM.

Figure 8. Sol-gel transition temperature control by mixing two polymers (II and III) aqueous solutions (29 wt %) with different transition temperatures. The legend indicates weight ratio of each polymer aqueous solution. The 100/0 and 0/100 are the G′ curves of polymer II and polymer III aqueous solution (29 wt %) showing solto-gel transition at 16 °C (289 K) and 49 °C (322 K), respectively. The mixture shows intermediate transition temperatures.

as ion-water dipole interactions, dipole-dipole interactions, and dipole-induced dipole interactions are affected by adding a salt to this system. Such resultant intermolecular forces contribute to the free energy of the system and are reflected in the change in the sol-to-gel transition temperature. The sol-to-gel transition temperature of the PLGA-gPEG polymer aqueous solution (25 wt %) decreased by 4-5 °C by increasing the ionic strength from 0 to 120 mM (Figure 7). Another method to control the sol-to-gel transition temperature is the use of the mixtures of miscible polymer aqueous solutions showing different sol-to-gel transition temperatures. The polymer (II/III) mixtures with ratios of 100/0, 70/30, 60/40, 50/50, and 0/100 were studied by dynamic mechanical analysis to test the miscibility of the systems and the possibility of controlling the sol-to-gel transitions. The transition temperatures were described by the following empirical equation 1/Ts-g ∼ W1/Ts-g1 + W2/Ts-g2

(2)

where W1, W2, Ts-g1, and Ts-g2 are weight fractions and the sol-to-gel transition temperatures (in K) of polymers II and III aqueous solutions (29 wt %), respectively. This equation was suggested for the prediction of the glass transition temperature of random copolymers consisting of two monomers or completely miscible blends of two polymers.18 The validity of this equation can serve as a basis for miscibility on the molecular level. As shown in Figure 8 and Table 2, the sol-to-gel transition temperatures were well described by this equation, indicating appropriate miscibility of the two polymers on the molecular level.

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Sol-Gel Transition Temperatures Table 2. Prediction of Sol-to-Gel Transition Temperature of Mixture of Two Polymers Aqueous Solutions polymer composition (II/III) 100/0

70/30

60/40

50/50

0/100

289

298.2 298

301.4 302

304.6 305

322

(K)a

calculated observed (K)

a 1/T s-g ∼ W1/Ts-g1 + W2/Ts-g2 where W1, W2, Ts-g1, and Ts-g2 are weight fractions and sol-to-gel transition temperatures (in K) of polymer II and III aqueous solutions (29 wt %), respectively.

Figure 9. UV-vis spectra showing the hydrophobic microenvironment formation with increasing PLGA-g-PEG copolymer (I) concentration in water. At the fixed concentration of dye (4 µM) and temperature (20 °C), polymer concentration varied from 0.01 to 0.25 wt %.

Figure 10. 13C NMR spectra of 25% (wt) PLGA-g-PEG (I) in D2O as a function of temperature. The zoomed spectra around 73 ppm are shown to the left. The sample was equilibrated for 15 min at each temperature before measurement. The 20 °C (sol phase), 33 °C (just above sol-to-gel transition), 40 °C (gel phase), and 50 °C (solsyneresis) are the various measured temperatures. The 13C NMR spectrum in CDCl3 at room temperature is also shown as a reference.

PLGA-g-PEG consists of hydrophobic PLGA and hydrophilic PEG. Due to amphiphilic nature of the polymer, the PLGA-g-PEG form micelles in water. The hydrophobic backbones occupy the core, and hydrophilic PEG grafts occupy the shell of a micelle. The formation of micelles was investigated by partitioning the hydrophobic dye (1,6diphenyl-1,3,5-hexatriene (DPH)) in the polymer solution. With increasing PLGA-g-PEG copolymer concentration in water, the absorbance at 315 nm decreases while absorbance at 356 nm increases (Figure 9). The formation of the hydrophobic microenvironment is responsible for the spectral changes, suggesting the micelle formation.6 13C NMR of PLGA-g-PEG polymer aqueous solution (25 wt %) shows such a core-shell structure (Figure 10). The methyl group (70.8 ppm) of PLGA and ethylene group (15 ppm) of PEG are shown as sharp peaks in CDCl3 because chloroform is a good solvent for PLGA and PEG. Both segments are in highly dynamic motion in chloroform and appear as sharp peaks in 13C NMR. However, in water the ethylene group (16-18 ppm) of PEG appears as a sharp peak, whereas the methyl group (72-73 ppm) of PLGA appears as a broadened and collapsed peak in the sol (20 °C) and gel states (33 and 40 °C), suggesting core-shell structure.10 With a further increase in temperature, the peak height of the PLGA methyl peak increases, and the PEG peak is split into two peaks, a sharp one at 72.4 ppm and a broad one at 72.7 ppm. This behavior is thought to be caused by an increase in molecular motion of the hydrophobic backbone and phase mixing between PEG and PLGA at higher (>50 °C) temperatures. This observation gives the molecular implication of sol and gel states. At the lowtemperature sol state, the PLGA-g-PEG is in dynamic equilibrium between unimers (nonassociated PLGA-g-PEG copolymer) and micelles. With increasing temperature, the

micelles undergo changes in aggregation to form a gel at the sol-to-gel transition temperature. At higher temperatures, the kinetic energy overcomes the constraints of micelle-based gel network, causing the system to flow and form a hightemperature sol phase. On the basis of this observation, two polymers with different sol-to-gel transition temperatures mixed on the molecular level and formed mixed micelles, resulting in single sol-to-gel transition. Therefore, we can prepare the aqueous polymer solution with a different sol-to-gel transition temperature by a simple mixing of two polymers with different sol-to-gel transition temperatures. The sol-to-gel transition temperature of the mixture can be predicted based on eq 2. The control of the sol-to-gel transition temperature is very important in biomedical applications, because it determines the formulation temperature. The drug, protein, or cellcontaining formulation should be mixed at the sol state and injected into a body to form a gel at body temperature. The sol-to-gel transition temperature determines the sterilization temperature. The aqueous polymer solution can be sterilized easily by syringe filtration through a 0.2 µm filter in the sol state. The initial burst of drug when this system is applied to a drug delivery system may be affected by kinetics of the sol-to-gel transition. The lower the sol-to-gel transition temperature, the faster the gelation and a decrease in the initial burst are expected. On the basis of the previous consideration, the optimization of a depot system for a specific application requires a system with an optimal solto-gel transition temperature. The fine tuning of the sol-togel transition could be realized by varying ionic strength of the PBS buffer and by mixing two polymer aqueous solutions with different sol-to-gel transition temperatures.

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Conclusions In this paper, we reported the thermogelling biodegradable polymer (PLGA-g-PEG) aqueous solution. The in situ gel formation was confirmed by injecting subcutaneously PLGAg-PEG copolymer aqueous solution in a rat model. The solto-gel transition temperature determined by the test tube inverting method, the falling ball method, and dynamic mechanical test were coincided within 1-2 °C. By varying ionic strength, the sol-to-gel transition temperature could be varied over a 4-5 °C temperature range. By choosing two different polymer aqueous solutions with different sol-togel transition temperatures, the sol-to-gel transition temperature of the mixture could be controlled in a predictable manner over a range of 15-50 °C. Acknowledgment. This work was supported by Pacific Northwest National Laboratory (PNNL)/Battelle Independent Research and Development funds. References and Notes (1) Bulmus, V.; Ding, Z.; Long, C. J.; Stayton, P. S.; Hoffman, A. S. Bioconjugate Chem. 2000, 11 (1), 78-83. (2) Zhang, J.; Peppas, N. A. Macromolecules 2000, 33, 102-107. (3) Linhard, J. G.; Tirrell, D. A. Langmuir 2000, 16, 122-127.

Chung et al. (4) Malmsten, M.; Lindman, B. Macromolecules 1992, 25, 5440-5446. (5) Mingvanish, W.; Mai, S. M.; Heatley, F.; Booth, C. J. Phys. Chem. B 1999, 103, 11269-11274. (6) Jeong, B.; Kibbey, M. R.; Birnbaum, J. C.; Won, Y. Y.; Gutowska, A. Macromolecules 2000, 33, 8317-8322. (7) Jeong, B.; Wang, L. Q.; Gutowska, A. Chem. Commun. 2001, 16, 1516-1517. (8) Gutowska, A.; Jeong, B.; Jasionowski, M. Anat. Rec. 2001, 263, 342349. (9) Jeong, B.; Bae, Y. H.; Kim, S. W. J. Controlled Release 2000, 63, 155-163. (10) Jeong, B.; Bae, Y. H.; Kim, S. W. Macromolecules 1999, 32 (21), 7064-7069. (11) Tanodekaew, S.; Godward, J.; Heatley, F.; Booth, C. Macromol. Chem. Phys. 1997, 198, 3385-3395. (12) Gilbert, J. C.; Richardson, J. L.; Davies, M. C.; Palin, K. J.; Hadgraft, J. J. Controlled Release 1987, 5, 113-118. (13) Yoshida, T.; Takahashi, M.; Hatakeyama, T.; Hatakeyama, H. Polymer 1998, 39, 1119-1122. (14) Wanka, G.; Hoffmann, H.; Ulbricht, W. Colloid Polymer Sci. 1990, 268, 101-117. (15) Olabisi, O.; Robeson, L. M.; Shaw, M. T. Polymer-polymer miscibility; Academic Press: New York, 1979; pp 281-287. (16) Cho, K. Y.; Kim, C. H.; Lee, J. W.; Park, J. K. Macromol. Rapid Commun. 1999, 20, 598-601. (17) Mott, R. L. Applied fluid mechanics, 3rd ed.; Merrill Publishing Co.: Columbus, OH, 1990; pp 33-34. (18) Rosen, S. L. Fundamental principles of polymeric materials; John & Wiley: New York, 1982; pp 94-95.

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