Cylindrical Polymer Brushes with Elastin-Like Polypeptide Side Chains

Jun 11, 2013 - Jonathan R. McDaniel,. ‡. Karl Fischer,. †. Ashutosh Chilkoti,. ‡,* and Manfred Schmidt†,*. †. Institute of Physical Chemistr...
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Article pubs.acs.org/Macromolecules

Cylindrical Polymer Brushes with Elastin-Like Polypeptide Side Chains Désirée Weller,†,§ Jonathan R. McDaniel,‡ Karl Fischer,† Ashutosh Chilkoti,‡,* and Manfred Schmidt†,* †

Institute of Physical Chemistry, University of Mainz, Jakob-Welder Weg 11, 55099 Mainz, Germany Department of Biomedical Engineering, Duke University, Durham, North Carolina 27708-0181, United States § Graduate School Materials Science in Mainz, Staudinger Weg 9, 55128 Mainz, Germany ‡

S Supporting Information *

ABSTRACT: Monodisperse high molar mass elastin-like polypeptide macromonomers comprising 20 pentasequences (M = 8332 g/mol) were radically polymerized to high degrees of polymerization Pw = 590. Polymerization was conducted in water well above the lower phase transition temperature, i.e., in the phase separated regime. The resulting polymers adopt a cylindrical shape as demonstrated by AFM pictures of solutions spin-cast on mica. The directional persistence of the cylindrical brushes was determined by static light scattering to Kuhn statistical segments lengths lk = 120 nm at 5 mM aqueous NaCl solution which decreased to lk = 54 nm at 0.65 M NaCl. Upon polymerization the phase transition temperature drops significantly and the transition interval becomes sharper. The change of the hydrodynamic radius of the cylindrical brushes was monitored by dynamic light scattering as a function of temperature and revealed a continuous decrease from 20 to 36 °C, above of which aggregates of several hundred nm in size start to form prior to phase separation.



INTRODUCTION Cylindrical brush polymers consist of a usually flexible main chain densely decorated with oligomeric/polymeric side chains. Because of the strong steric repulsion between the side chains, the main chain is forced into an extended wormlike conformation of considerable directional persistence leading to Kuhn statistical segment lengths of 10 nm < lk < 100 nm, depending on the side chain length and solvent quality.1−11 In contrast, cylindrical brushes of a synthetic polymer with a polypeptide side-chain are rare.12−19 As opposed to cylindrical brushes prepared by “grafting from” polymerization of the side chains from a macroinitiator which leads to more or less narrow but still polydisperse side chains, “grafting through” polymerization of monodisperse macromonomers yields cylindrical brushes with monodisperse side chains. However, the latter approach inevitably leads to broad main chain length distributions. So far, monodisperse macromonomers of small molar masses could be prepared by tedious fractionation procedures, for examples polystyrene macromonomers with Pn < 84 or utilizing elastin-like polypeptide (ELP) comprising one pentasequence.17−19 The motivation of this work is to synthesize hybrid polymer brushes where the side chains are composed of a high molar mass and monodisperse elastin-like polypeptide (ELP) by grafting through wherein the peptide polymer is converted into a reactive vinyl macromonomer for free radical polymerization similar to previous work with ELP.17−19 ELPs are peptide polymers of the pentapeptide repeat unit Val-Pro-Gly-Xaa-Gly, where Xaa can be any residue except © 2013 American Chemical Society

proline. ELPs are highly soluble in aqueous solutions, but upon raising the temperature, ELPs undergo hydrophobic collapse accompanied by aggregation.20−22 This behavior is fully reversible on lowering the temperature.23−25 The phase transition temperature of an ELP can also be tuned by solution conditions such as the type and concentration of salt.26,27 We chose an ELP as the macromonomer to grow a cylindrical polymer brush because of the following reasons: (1) The chain lengths of ELPs can be precisely specified at the gene level; (2) the resulting polypeptide is monodisperse; (3) the absolute control over ELP sequence by genetically encoded synthesis means that the number and locations of the reactive side chainshere the amine end-groupscan be precisely specified; and (4) the LCST behavior of the ELP provides a variable to further tune the architecture of the cylindrical polymer brush. With these polymers, we elucidate the conformation and the chain stiffness of cylindrical brush polymers with elastin-like polypeptide (ELP) side chains as well as to study the influence of polymerization (i.e., the local overcrowding of the densely grafted ELP side chains) on the phase behavior. We show herein that high molar mass and monodisperse ELP macromonomers can be synthesized that upon successful polymerization yield cylindrical brushes that are sensitive to temperature and to added salt. Received: May 2, 2013 Revised: June 4, 2013 Published: June 11, 2013 4966

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Scheme 1. Synthesis Route of Cylindrical Brush Polymers with ELP Side Chains



reaction mixture was diluted with water (30 mL) and the residual monomer was removed by dialysis (Amicon Centrifuge Tubes, 30K). After freeze-drying a colorless solid was obtained. Yield: 72% (0.96 g). Poly(methacryloyl-ELP) was soluble in water and could be analyzed by static and dynamic light scattering. ELP Characterization. The purity of the ELPs was assessed by performing SDS-PAGE using Bio-Rad Ready Gels with a 4−20% Tris gradient. The gels were visualized by copper staining (0.5 M CuCl2). MALDI−MS was performed on a PE Biosystems Voyager-DE instrument equipped with a nitrogen laser (337 nm). The MALDI− MS samples were prepared in a 50% (v/v) aqueous acetonitrile solution containing 0.1% trifluoroacetic acid, diluted into a sinapinic acid matrix. Turbidity Measurements. The inverse transition temperature was obtained by measuring the turbidity profile at 345 nm on a temperature-controlled Cary 100 Bio UV−VIS spectrometer (Varian, Inc.). The sample was heated at 1 °C·min−1 and ranged in concentration from 0.01 to 1 g·L−1. Measurements were performed in different salt solutions. The Tt was defined as the temperature that corresponds to the maximum of the first derivative of its turbidity profile with respect to temperature, which is indicative of the onset of the phase transition. Static and Dynamic Light Scattering. Static light scattering (SLS) measurements were performed with an ALV-SP86 goniometer, an ALV-3000 correlator, a Uniphase HeNe Laser (25 mW output power at λ = 632.8 nm wavelength) and an ALV/High QE APD avalanche diode fiber optic detection system. Dynamic light scattering measurements for the ELP and ELP macromonomer were also performed on this instrument setup. An ALV-SP125 goniometer, an ALV-5000 correlator and a Spectra Physics 2060 Argon ion laser (500 mW output power at λ = 514.5 nm wavelength) were utilized for dynamic light scattering (DLS) measurements. The scattered intensity was divided by a beam splitter (approximately 50:50), each portion of which was detected by a photomultiplier. The two signals were crosscorrelated in order to minimize nonrandom electronic noise. Temperature dependent dynamic light scattering was measured with a HeNe laser (632.8 nm, 25 mW output power), an ALV-CGS 8F SLS/DLS 5022F goniometer equipped with eight simultaneously working ALV 7004 correlators, and eight QEAPD Avalanche photodiode detectors. Solutions were typically measured from 30° to 150° in steps of 5° (SLS) or in steps of 5° or 20° (DLS). The static scattering intensities were analyzed according to Zimm in order to yield the weight-average molar mass, Mw, the square root of z-average mean square radius of

EXPERIMENTAL SECTION

Materials. Restriction enzymes and calf intestinal phosphatase (CIP) were purchased from New England Biolabs (Ipswich, MA), T4 DNA ligase from Invitrogen (Carlsbad, CA) and the pET-24a+ cloning vector from Novagen Inc. (Madison, WI). All custom oligonucleotides were synthesized by Integrated DNA Technologies Inc. (Coralville, IA). EB5α and BL21 Escherichia coli cells were purchased from Edge BioSystems (Gaithersburg, MD). All E. coli cultures were grown in TBDry media (MO BIO Laboratories, Inc., Carlsbad, CA). The DNA miniprep, gel purification, and PCR purification kits were received from Qiagen Inc. (Germantown, MD). Methacrylic acid, N-hydroxysuccinimide ester, 4,4-azobis-4-cyanovaleric acid, and NEt3 were purchased from Sigma-Aldrich (St. Louis, MO). Synthesis of ELP E4−20 in JMD5 (3). ELP was synthesized from purchased oligomers using plasmid reconstruction recursive directional ligation (further information can be found in the Supporting Information).28 ELP was recombinantly expressed from E. coli bearing a modified pET-24a+expression vector28 and purified using inverse transition cycling.24 Synthesis of Methacryloyl-ELP (4). The N-hydroxysuccinimide ester of the methacrylic acid (2) was synthesized according to the procedure described by Batz et al.29 The synthesis of methacryloylELP was performed under argon atmosphere in waterfree DMF. To a solution of E4−20 JMD5 (3) in DMF (25.2 mL) was added Nhydroxysuccinimide ester of methacrylic acid (3.97 g, 21.93 mmol), dissolved in DMF (9 mL). After addition of NEt3 (2.73 mL, 19.5 mmol) in DMF (1.8 mL), the reaction mixture was stirred for 24 h in the absence of light. DMF was removed under vacuum. To obtain the pure product (4) dialysis was conducted in a methanol/water = 3/1 mixture using a Spectra/Por dialysis membrane MWCO: 1000 g·mol−1. The solvent was removed under vacuum and the pure product was obtained as a solid. Yield: 1.38 g (76%). HPLC elution curve for methacryloyl-ELP and MALDI-TOF spectra are shown in the Supporting Information as Figures S1 and S2. MALDI: ELP + Na+, 8364 g·mol−1. Synthesis of Poly(methacryloyl-ELP) (6). In a typical polymerization reaction, the initiator 4,4-azobis-4-cyano valeric acid (5) (0.22 mg, 8.0 × 10−4 mmol =0.5 mol % with respect to monomer), dissolved in water (4 mL), was added to the dry monomer (4) (1.33 g, 0.16 mmol), resulting in a polymerization solution with a macromonomer concentration of 4.0 × 10−2 mol·L−1, i.e. 25% (w/w). The solution was degassed by three freeze pump cycles and subsequently polymerized at 70 °C, above the phase transition temperature, for 19 h. Then the 4967

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gyration, Rg = ⟨Rg2⟩z1/2, and the second viral coefficient A2. The experimental uncertainties are estimated to be ±5% for Mw and Rg. The correlation functions showed a monomodal decay and were fitted by a sum of two exponentials, from which the first cumulant Γ was calculated. The z-average diffusion coefficient Dz was obtained by extrapolation of Γ/q2 for to q = 0 leading to the inverse z-average hydrodynamic radius Rh = ⟨1/Rh⟩z−1 by formal application of Stokes law. The experimental uncertainties are estimated to ±2% for Rh. Stock solutions of each sample were prepared at c = 1 g·L−1 and filtered through 0.2 μm pore size Millipore GV filters (for the ELP polymer brush) or 0.1 μm pore size Anotop filters (for the ELP and ELP macromonomer) into 20 mm diameter quartz cuvettes (Hellma). Further dilutions were made by subsequent addition of 0.1 μm pore size Millipore VV filtered solvent into the LS cuvette and the respective concentrations were obtained by weighing. The refractive index increments at λ = 632.8 nm wavelength were measured by a home-built Michelson interferometer as described elsewhere.30 The values for dn/dc were determined to be 0.1548 × 10−3 g·dm−3 for the polymer in water. The experimental uncertainties are estimated to ±2% for dn/dc. Atomic Force Microscopy. Measurements were performed using a Veeco MultiMode scanning probe microscope and a Nanoscope IIIa controller. All micrographs were taken in the tapping mode. An Olympus OMCL-AC160-W2 cantilever with a resonance frequency of 300 kHz (spring constant 42 N·m−1) was used. For the measurement, the sample, c = 0.1 g·L−1 in water, was spin coated on mica. CD Measurements. Spectra were measured on a Jasco J-815 spectrometer equipped with a Peltier element and a solid-state detector at wavelengths from 190 to 260 nm. Measurements were performed in the continuous scan mode with a scan rate of 50 nm·min−1 and a bandwidth of 1 nm. One mm cuvettes were filled with 400 μL of sample solution with the concentration of 0.1 g·L−1. Spectra were recorded in the temperature range of 20−80 °C.

macromonomer macromonomer by dialysis (as proven by capillary electrophoresis, see Supporting Information, Figure S8) the cylindrical brush polymer was characterized by static and dynamic light scattering, AFM and CD-spectroscopy. The Zimm-plot in 2 mM NaCl solution is shown in Figure 1 and the results are summarized in Table 1.

Figure 1. Zimm plot of the cylindrical brush with ELP side chains in 2 mM aqueous NaCl solution.

The main chain degree of polymerization Pw = 590 is very high given the high ELP molar mass. This may indicate that the spherical micelles do not persist at the polymerization conditions, but possibly form cylindrical micelles at higher concentration and/or temperature, which in turn would facilitate polymerization to high molar mass polymers as was already speculated for extremely high molar mass PEO macromonomers.35 In any event, the cylindrical nature of the polymer is clearly seen in the AFM picture taken from spincast aqueous solution onto mica (see Figure 2). The molar mass distribution could



RESULTS AND DISCUSSION Cylindrical brush polymers with ELP side chains were prepared according to Scheme 1. The NHS-ester 2 was coupled to the N-terminus of ELP comprising 20 amino acid pentasequences (i.e., 100 amino acids) in order to yield the macromonomer 4. As shown in Table 1 and in the Supporting Information the Table 1. Characterization Data of ELP Macromonomer and Resulting Cylindrical Brush Polymer sample ELP ELP macromonomer ELP polymer brush a

Mw/g·mol−1 a

8264 8332a 4.9 × 106

Rh/nm

Rg/nm

A2/mol·cm3·g−2

2.5 3.4 35.2

− − 51.7

− − 3.67 × 10−5

Determined by MALDI−TOF.

macromonomer exhibits a significantly larger hydrodynamic radius, Rh = 3.4 nm, as compared to the pure ELP, Rh = 2.4 nm. Since the latter value coincides well with data published previously31 the larger radius of the macromonomer indicates the formation of spherical micelles in dilute solution. As known from previous work high molar mass macromonomers are difficult to polymerize and require an extremely high concentration of macromonomer in order to obtain high main chain degrees of polymerization and unusually long polymerization time.32,33 Therefore, the polymerization was conducted at 70 °C where the highly concentrated macromonomer solution becomes phase separated. Thus, the polymerization reaction primarily proceeds in the even higher concentrated gel phase, which was applied recently to polymerize poly-2-isopropropyloxazoline macromonomers to high molar mass cylindrical brushes.34 After removal of residual

Figure 2. AFM picture taken from spincast aqueous solution onto mica.

not be quantified, as all attempts to obtain GPC traces failed so far, because of strong adsorption on the GPC columns. As seen in the AFM images, the distribution is quite broad as expected for free radical polymerization. A closer inspection of the AFM pictures reveals that the majority of the long main chain polymers seem to be fractured into several pieces on the surface. In order to confirm this impression AFM-pictures with a lower surface coverage were recorded. As shown in the 4968

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the macromonomer the concentration dependence is much smaller which is qualitatively explained by the high local ELP concentration within the cylindrical brush.

Supporting Information (Figure S10) the main chain is broken into several pieces. As indicated by the low height of the cylindrical brushes of 1−1.2 nm, only, the surface-polymer interaction could be so strong that chemical main chain bonds are broken as reported before on cylindrical brushes with poly butyl methacrylate side chains on the air−water interface.36,37 The width of the cylindrical brushes is approximately 17 nm which corresponds to twice the mean end-to-end distance of the ELP side chains. A qualitative measure for the size distribution may be obtained from the second cumulants obtained by the fit of the DLS correlation functions which scatters around 0.2, a value somewhat larger as expected for a Schulz−Flory distribution. The phase transition temperature of ELP is known to strongly depend on ELP concentration and on added salt. The ELP macromonomer was chosen such that the phase transition temperature in pure water is high, but upon addition of 0.75 to 1.5 M NaCl the transition temperature drops to a regime between 25 to 50 °C depending on the macromonomer concentration as shown in Figure 3. It should be noted that the

Figure 5. Transition temperature versus concentration for the ELP brush in 0.15 PBS.

Similar arguments were put forward in order to explain the lower phase transition temperatures observed for ELP micelles as compared to single ELP chains.38,39 It should be noted that the concentration of ELP in the cylindrical brush corona is estimated to be as high as 30 mM, if the brush diameter is taken as d = 30 nm (see Table 2, below). Table 2. Ionic Strength Dependence of the Kuhn Statistical Segment Length, lk, and of the Hydrodynamically Effective Diameter, d, of the ELP Cylindrical Brush

Figure 3. Phase transition temperature as a function of ELP macromonomer concentration for different added NaCl concentrations.

c(NaCl)/mM

lk/nm

d/nm

2 10 48 155 640

120 90 75 65 54

30 30 28 28 22

Often the “sharpness” of the phase transition is discussed on the basis of turbidity measurements, which depends on the aggregation kinetics in the spinodal/bimodal regime.40 The kinetics in turn may depend on the width of the spinodal regime, on concentration and on the heating rate. For the ELP brushes, a very large concentration dependence of the turbidity curves is observed (see Supporting Information, Figure S4). At 1 g·L−1 the transition is extremely sharp (ΔT = 0.5 °C) but becomes shallow at c = 0.01 g·L−1 (ΔT > 4 °C). Also, little hysteresis is observed by turbidity between heating and cooling except for some broadening in the cooling curves (see Supporting Information, Figure S9). In order to more quantitatively investigate the temperature and salt dependent conformation of the cylindrical brush polymer static and dynamic light scattering was employed. In Figure 6, the respective dimensions of the brush are shown as a function of added NaCl. Both quantities are observed to shrink with added salt. A quantitative analysis utilizing the wormlike chain model41,42 reveals the Kuhn statistical segment length to decrease from lk = 120 nm at 2 mM NaCl to lk = 65 nm in 0.64 M NaCl solution. Within experimental uncertainty the hydrodynamically effective cross-section of the brush remains constant at d = 30 nm which is a significantly larger than twice the end-to-end distance, 2⟨R2⟩1/2 = 18 nm, of the respective linear ELP chain. As ELP is barely charged except for the C-

transition temperature of the macromonomer is somewhat lower as compared to the pure ELP, consistent with the conversion of the polar N-terminus to the more hydropohic methacryloyl-ELP. In contrast to the ELP macromonomer, the ELP cylindrical brush polymer has a much lower phase transition temperature, but almost no change of the transition temperature with polymer concentration (see Figures 4 and 5). As compared to

Figure 4. Difference of the phase transition temperature for the ELP macromonomer (black curve) and the ELP cylindrical brush polymer (red curve) in 0.15 M PBS at c = 1 g·L−1. Heating rate: 1 °C·min−1. 4969

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nm in size) and at T > 37 °C no single brush polymers are detectable by light scattering, anymore. CD spectroscopy (Figure 8) indicates an increase of the βturn content with increasing temperature, which is much more

Figure 6. Hydrodynamic radius and radius of gyration as a function of added NaCl concentration.

terminus the strong dependence of the chain stiffness on ionic strength is difficult to explain in terms of electrostatic interaction, because even at 2 mM salt the Debye screening length is less than 10 nm which is similar to the mean distance of the charged side chain end from the polymer backbone. An alternative explanation could be that the attraction between the ELP side chains increases with increasing salt concentration, which may reduce the repulsive forces responsible for either the extension of the main chain (i.e., the length of the cylinder) or for the directional persistence of the main chain at constant cylinder length. In order to distinguish between the two possibilities SANS or SAXS measurements are required, which is beyond the scope of the present work. Assuming a change of the persistence length at constant maximum contour length, Lw = bPw = 147 nm (b = 0.25 nm, the length of a vinylic repeat unit), of the cylinders the Kratky−Porod wormlike chain model can be applied to derive the Kuhn statistical segment length and the hydrodynamically effective diameter of the cylinder from the measured Rg and Rh values shown in Figure 6. The results are summarized in Table 2. It is interesting to note that the hydrodynamically effective diameter, i.e. the side chain extension, remains constant up to 0.15 M added salt at d = 30 nm and shrinks to d = 22 nm at 0.64 M added salt. The Kuhn statistical segment length varies from lk = 120 nm at 2 mM added salt to lk = 54 nm, thus lying in a regime reported for comparable cylindrical brush polymers. Likewise, the size of the cylindrical brush polymer also depends on the temperature. In Figure 7, the hydrodynamic radius is plotted as a function of temperature in 0.15 M PBS. At 36.5 °C the cylindrical brushes start to rapidly aggregate (>200

Figure 8. CD spectra of ELP macromonomer (M) and ELP cylindrical polymer brush (P) taken at c = 0.1 g·L−1 and different temperatures in water.

pronounced for the cylindrical brushes as compared to the ELP macromonomer.43 Both, cylindrical brushes and macromonomer show isosbestic points which is 1 nm lower for the macromonomer (for a better resolution of the isosbestic points see separate plots in the Supporting Information). Similar curves are also obtained by increasing the salt content (see Supporting Information, Figure S7c). This difference between macromonomer and cylindrical brush is most probably within experimental uncertainty, but the spectra clearly indicate a defined transition of the coil fraction into more ordered βturns.



CONCLUSION The present work, demonstrates that high molar mass cylindrical brush polymers with polypeptide side chains can be obtained by polymerization of the respective macromonomers. It confirms the results of a recent study on cylindrical brushes with poly oxazoline side chains34 that polymerization in the concentrated phase of a phase separated solution is advantageous for obtaining high degrees of main chain polymerization. Because of the long side chains comprising 100 peptide repeat units the Kuhn statistical segment length is as large as lk = 120 nm which continuously decreases with increasing ionic strength, i.e., with decreasing solvent quality for the side chains. Apparently, the decreasing repulsion between the side chains leads to an increase of main chain flexibility. In future experiments cylindrical brush polymers with ELP side chains will be utilized in biomedical applications because (i) the ELP side chains are biocompatible and (ii) the C-terminus of each side chain offers a variety of conjugation reactions for biologically active molecules.



ASSOCIATED CONTENT

* Supporting Information S

ELP synthesis, CD spectra, HPLC curves, DLS correlation functions, MALDI−TOF spectra, turbidity curves, AFM pictures and electrophoretic mobilities. This material is available free of charge via the Internet at http://pubs.acs. org/.

Figure 7. Hydrodynamic radius as a function of temperature for the ELP brush in 0.15 M PBS at c = 0.019 g·L−1. 4970

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(26) Cho, Y.; Zhang, Y.; Christensen, T.; Sagle, L. B.; Chilkoti, A.; Cremer, P. S. J. Phys. Chem. B. 2008, 112 (44), 13765−13771. (27) Urry, D. W. Angew. Chem., Int. Ed. Engl. 1993, 32 (6), 819−841. (28) McDaniel, J. R.; MacKay, J. A.; Quiroz, F. G.; Chilkoti, A. Biomacromolecules 2010, 11 (4), 944−952. (29) Batz, H.-G.; Franzmann, G.; Ringsdorf, H. Angew. Chem., Int. Ed. Engl. 1972, 11 (12), 1103−1104. (30) Becker, A.; Köhler, W.; Müller, B. Ber. Bunsen-Ges. Phys. Chem. 1995, 99 (4), 600−608. (31) Fluegel, S.; Fischer, K.; McDaniel, J. R.; Chilkoti, A.; Schmidt, M. Biomacromolecules 2010, 11 (11), 3216−3218. (32) Tsukahara, Y.; Mizuno, K.; Segawa, A.; Yamashita, Y. Macromolecules 1989, 22 (4), 1546−1552. (33) Tsukahara, Y.; Tsutsumi, K.; Yamashita, Y.; Shimada, S. Macromolecules 1990, 23 (25), 5201−5208. (34) Bühler, J.; Muth, S.; Fischer, K.; Schmidt, M. Macromol. Rapid Commun. 2013, 34, 588−594. (35) Kawaguchi, S.; Schmidt, M. Polym. J. 2002, 34 (4), 253−260. (36) Sheiko, S. S.; Frank, C. S.; Randall, A.; Shirvanyants, D.; Rubinstein, M.; Hyung-il, L.; Matyjaszewski, K. Nature 2006, 440, 191−194. (37) Lebedeva, N. V.; Frank, C. S.; Hyung-il, L.; Matyjaszewski, K.; Sheiko, S. S. J. Am. Chem. Soc. 2008, 130 (13), 4228−4429. (38) McDaniel, J. R.; Bhattacharyya, J.; Vargo, K. B.; Hassouneh, W.; Hammer, D. A.; Chilkoti, A. Angew. Chem., Int. Ed. 2013, 52 (6), 1683−1687. (39) McDaniel, J. R.; MacEwan, S. R.; Dewhirst, M.; Chilkoti, A. J. Controlled Release 2012, 159 (3), 362−367. (40) Li, W.; Zhang, A.; Feldman, K.; Walde, P.; Schlüter, A. D. Macromolecules 2008, 41 (10), 3659−3667. (41) Kratky, O.; Porod, G. Recl. Trav. Chim. Pays-Bas 1949, 68 (12), 1106−1122. (42) Schmidt, M. Macromolecules 1984, 17 (4), 553−560. (43) Urry, D. W.; Trapane, T. L.; Prasad, K. U. Biopolymers 1985, 24 (12), 2345−2356.

AUTHOR INFORMATION

Corresponding Author

*(M.S.) E-mail: [email protected]. Notes

The authors declare no competing financial interest.



ACKNOWLEDGMENTS D.W. is grateful for receiving a personal stipend from the Graduate School “Materials Science in Mainz. This work was financially supported by the “Center of Complex Matter”, University Mainz.



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