pH- and Ionic-Strength-Induced Contraction of Polybasic Micelles in

Apr 10, 2015 - These systems are also sensitive to changes in the solution pH, which ..... Both the TEM and DLS data exhibit narrow dispersities (dist...
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pH- and Ionic-Strength-Induced Contraction of Polybasic Micelles in Buffered Aqueous Solutions Jennifer E. Laaser,† Yaming Jiang,‡ Dustin Sprouse,† Theresa M. Reineke,† and Timothy P. Lodge*,†,‡ †

Department of Chemistry and ‡Department of Chemical Engineering & Materials Science, University of Minnesota, Minneapolis, Minnesota 55455, United States S Supporting Information *

ABSTRACT: We report the synthesis and characterization of poly(dimethylaminoethyl methacrylate)-block-poly(styrene) (PDMAEMA-b-PS) diblock copolymers by RAFT polymerization. These polymers form uniform spherical micelles with dispersities less than 0.05 upon addition of aqueous buffer to polymer solutions in DMF. Potentiometric titrations under constant ionic strength conditions yield the first rigorous ionicstrength-effective pKa correspondence for PDMAEMA homopolymers and micelles. We demonstrate that the effective polymer pKa increases monotonically toward the monomer pKa with increasing ionic strength, but decreases slightly upon association of polymer chains into micelles. We further characterize the pH- and ionic-strength-induced contraction of the micelle coronas in buffered aqueous solutions. In monoprotic buffers, the micelle corona behaves as a salted osmotic brush, as has been observed for other block polyelectrolyte micelle systems in unbuffered solutions. In polyprotic buffers, however, we observe an anomalously high degree of corona contraction. We demonstrate through a simple two-domain equilibrium model that this contraction likely arises from concentration of the charged buffer species in the micelle corona, which shifts the buffer dissociation equilibrium farther toward multivalent species than in the bulk.

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fixed, these brushes are not pH-responsive, but they are sensitive to ionic strength and will begin to collapse when the bulk salt concentration increases and the differential osmotic pressure keeping the brush extended decreases.13−15 Weak or “annealed” polyelectrolytes, such as poly(acrylic acid) and unquaternized polyamines, in which the charges are generated by dynamic acid−base equilibria, exhibit similar ionic strength response. These systems are also sensitive to changes in the solution pH, which lead to changes in the degree of protonation and the corresponding counterion concentration within the brush.12,16−18 Poly(dimethylaminoethyl methacrylate) (PDMAEMA) is a polycation that has been examined for nucleic acid delivery applications and exhibits high nucleic acid delivery efficiency.19−21 It also exhibits pH- and thermoresponsive behavior, with a lower critical solution temperature (LCST) near body temperature, making it an attractive target for both fundamental physical studies and biomedical22−25 and materials26,27 applications. Several groups have studied the protonation and micellization behavior of PDMAEMA homopolymers and copolymers. Recent reports demonstrate that the effective pKa of the homopolymer can be up to 2 pH units below that of the monomer19,28,29 and increases toward the

INTRODUCTION Polyelectrolytes have a wide range of useful properties for many applications, including high water solubility, sensitivity to pH and ionic strength, and the ability to complex with oppositely charged ions and macromolecules.1,2 Polyelectrolyte brushes,3 in which a polyelectrolyte layer is grafted to a planar or curved surface, or self-assembled from amphiphilic block copolymers, have found use in many applications such as controlling surface wetting,4 stabilizing colloidal dispersions,5 and as lubricants.6−8 Recently, spherical polyelectrolyte brushes and block copolymer micelles with polyelectrolyte coronas have also shown significant promise in biomedical applications such as drug and nucleic acid delivery.9,10 Understanding the fundamental physical behavior of the polyelectrolyte brush/micelle corona is critical for developing and refining applications using these materials. Spherical polyelectrolyte brushes and block copolymer micelles with polyelectrolyte coronas have thus been the subject of much fundamental experimental and theoretical work in the past 20 years.11 These brushes exhibit different behaviors depending on the nature of the charges in the polyelectrolyte chain. In strong polyelectrolytes, such as poly(styrenesulfonate) and quaternized polyamines, the charges are effectively fixed in place along the polymer chain. These systems are welldescribed as osmotic brushes, in which the osmotic pressure of counterions within the brush keeps the brush extended away from the surface or micelle core.12 Because the charges are © 2015 American Chemical Society

Received: February 18, 2015 Revised: March 31, 2015 Published: April 10, 2015 2677

DOI: 10.1021/acs.macromol.5b00360 Macromolecules 2015, 48, 2677−2685

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Macromolecules Scheme 1. Synthesis of (a) Poly(dimethylaminoethyl methacrylate) Macroinitiators and (b) Poly(dimethylaminoethyl methacrylate)-b-poly(styrene) Diblock Copolymers via RAFT Polymerization with the CPDT Chain-Transfer Agent

monomer pKa with increasing ionic strength,28 consistent with prior reports on titration of weak polyelectrolytes.30 Copolymerization with a hydrophobic monomer has also been shown to increase the pKa and decrease the LCST.29 To our knowledge the protonation behavior has not yet been studied in block copolymers that form spherical brushlike micelles, where the effective pKa should be shifted due to the high effective concentration in the micelle corona.31,32 Many of these studies on PDMAEMA protonation behavior, however, do not appear to have been conducted under constant ionic strength conditions, and it is important to fully characterize the ionicstrength-dependent protonation behavior to facilitate development of practical applications. Micellization of PDMAEMAbased block copolymers has been studied with both hydrophobic and pH-responsive cores,33−36 though primarily with a focus on the micellization process, rather than the corona behavior investigated in this study. The majority of studies of polyelectrolyte brushes to date have investigated behavior in unbuffered solutions. A few reports have investigated binding of spherical polyelectrolyte brushes with small proteins in buffered solution, but these reports focused on the binding process rather than on the behavior of the brush itself.37 However, the behavior of spherical polyelectrolyte brushes in buffered systems is critical for many applications. Biological systems, for example, are almost always buffered; blood, with pH ≈ 7.4, is buffered predominantly by carbonate and phosphate moieties.38 Importantly, both of these buffers are polyprotic and can generate neutral, monovalent, divalent, or even trivalent anions depending on the solution conditions. Several studies have shown that multivalent counterions lead to collapse of both planar and spherical polyelectrolyte brushes,39−41 an effect that is attributed to a decrease in the osmotic pressure inside the brush when monovalent counterions are replaced by a smaller number of their multivalent counterparts.39 Furthermore, because counterions accumulate in polyelectrolyte brushes, the buffer equilibria may be shifted inside the brush relative to the bulk.31 How these interactions may affect the polyelectrolyte brush behavior and how they vary with buffer and ionic strength are key points that will affect use of polyelectrolyte brushes in biological systems. In the first part of this paper, we describe the synthesis of PDMAEMA homopolymers and poly(dimethylaminoethyl methacrylate)-b-poly(styrene) (PDMAEMA-b-PS) block copolymers by reversible addition−fragmentation chain-transfer

(RAFT) polymerization, and characterize of their protonation behavior and micelle corona conformations as a function of pH and ionic strength. In the second part of the paper, we examine how polyprotic buffers affect spherical polyelectrolyte brushes formed from these polymers and discuss whether polyprotic buffer effects are likely to be important in brushes used for physiological applications.

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MATERIALS AND METHODS

Polymer Synthesis. Two PDMAEMA-b-PS block copolymers were synthesized by a two-step RAFT polymerization procedure adapted from the literature,42−44 as shown in Scheme 1. The 4-cyano4-[(dodecylsulfanylthiocarbonyl)sulfanyl]pentanoic acid chain-transfer agent (CPDT) and 4,4′-azobis(4-cyanovaleric acid) (V501) were used as received from Sigma-Aldrich. Azobis(isobutyronitrile) (AIBN) was recrystallized from methanol before use. 2-(Dimethylamino)ethyl methacrylate (DMAEMA) and styrene were passed through activated neutral alumina to remove inhibitors immediately prior to polymerization. PDMAEMA macroinitiators were first synthesized via RAFT polymerization of DMAEMA with CPDT. In a typical polymerization targeting a 30 kg/mol macroinitiator, DMAEMA (17.22 g, 0.110 mol), CPDT (163.6 mg, 0.405 mmol), and V501 (10.8 mg, 0.039 mmol) were combined with 33.80 g of toluene in a Schlenk flask. Three freeze−pump−thaw cycles were performed, after which the flask was filled with Ar, sealed, and removed from the vacuum line. The reaction mixture was stirred at 80 °C for 18 h, after which the reaction was quenched by placing the flask in an ice bath. The product was precipitated directly into ice-cold hexanes, redissolved in toluene, precipitated a second time into hexanes, and freeze-dried from benzene to yield a pale yellow powder. PDMAEMA-b-PS block copolymers were then synthesized following a similar procedure using the PDMAEMA macroinitiator in place of the CPDT chain-transfer agent. Styrene (14.86 g, 0.143 mol), PDMAEMA-CTA (6.000 g, 0.179 mmol), and AIBN (3.3 mg, 0.020 mmol) were combined with 18.85 g of toluene in a Schlenk flask. The flask and its contents were degassed via three freeze− pump−thaw cycles, filled with Ar, removed from the vacuum line, and polymerized at 80 °C for 20 h. The diblock copolymer was precipitated twice from hexanes and freeze-dried from benzene to yield a pale yellow powder. The molecular weight distributions and compositions of the products were determined by size-exclusion chromatography (SEC) and 1H nuclear magnetic resonance spectroscopy (NMR). SEC measurements were performed at room temperature on an Agilent 1200 Infinity series system with a multiangle light scattering detector (Wyatt Technology Dawn DSP-F) at room temperature with THF containing 1 wt % tetramethylethylenediamine as the eluent. The literature refractive index increment (dn/dc) of 0.186 mL/g was used 2678

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Macromolecules for PS,45 while that for PDMAEMA was measured by direct injection of stock solutions through the SEC RI detector (Wyatt Optilab DSP), yielding a value of 0.086 ± 0.002 mL/g. 1H NMR measurements were performed on a Varian Inova 500 MHz instrument. UV−vis measurements were also made using a Shimadzu spectrophotometer to assess retention of the trithiocarbonate moiety in the RAFT agent. SEC, NMR, and UV−vis traces for both macroinitiators and diblock copolymers are provided in the Supporting Information. The synthesized macroinitiators were PDMAEMA(18) (Mn = 18 kg/mol, Đ = 1.07) and PDMAEMA(34) (Mn = 34 kg/mol, Đ = 1.08), and the diblock copolymers were PDMAEMA(18)-b-PS(14) (Mn = 32 kg/ mol, Đ = 1.12) and PDMAEMA(34)-b-PS(12) (Mn = 46 kg/mol, Đ = 1.13), where the numbers in parentheses signify the number-average molecular weight of the corresponding block in kg/mol. These molecular weights correspond to number-average degrees of polymerization of approximately 115 for the PDMAEMA block and 135 for the PS block in the PDMAEMA(18)-b-PS(14) polymer and 217 for the PDMAEMA block and 115 for the PS block in the PDMAEMA(34)-bPS(12) polymer. A complete summary of the polymers used in this study is provided in the Supporting Information (Table S1). UV−vis showed no significant degradation of the RAFT agent following either step of the polymerization. Micelle Formation. PDMAEMA-b-PS micelles were prepared using the cosolvent method, which produces spherical micelles with frozen PS cores.46 Solutions of PDMAEMA-b-PS block copolymers were prepared at a concentration of 6 mg/mL in dimethylformamide. An equal volume of 100 mM TRIS buffer at pH 7.25 was added dropwise while stirring. Typically, the solution was initially transparent and became translucent after addition of approximately 10% of the total volume of buffer, indicating micelle formation. The solution was then diluted 2-fold, transferred to dialysis bags treated to remove heavy metals, and dialyzed into the final buffer for analysis. All buffers were prepared using Milli-Q water and approximately 20 mM buffer salt; a list of buffer salts and concentrations used at each pH and ionic strength is included in the Supporting Information (Tables S3 and S4). The final total ionic strength of the buffers was achieved by addition of sodium chloride. Samples were dialyzed against four changes of a 100-fold volume excess of buffer over 48 h before analysis. Cryogenic Transmission Electron Microscopy. The morphologies of PDMAEMA-b-PS micelles in aqueous buffer were examined by cryo-TEM. For each specimen, 3.5−4 μL of solution was loaded onto a carbon-coated and lacey film-supported copper TEM grid in the climate chamber of a FEI Vitrobot Mark III vitrification robot. The climate chamber was kept at 26 °C with saturated water vapor. The grid loaded with solution was blotted for 5 s and rested for 1 s before it was plunged into liquid ethane, which was kept around its freezing point by liquid N2. Vitrified samples were kept under liquid N2 before imaging. Cryo-TEM imaging was performed using a FEI Tecnai G2 Spirit BioTWIN equipped with an Eagle 4 megapixel CCD camera. The microscope was operated at 120 kV, and the specimen was held by a single tilt cryo-holder. Images were taken at an underfocus for adequate phase contrast. Background correction, thresholding, and region detection routines were applied in MATLAB to extract core size distributions. Potentiometric Titrations. Effective pKa values were determined via potentiometric titrations of polymer solutions in 20 mM HCl with 20 mM NaOH, with sodium chloride added to set the total ionic strength. Acid, base, and polymer concentrations were chosen such that the ionic strength varied by only 1 mM over the pH range of interest (see Supporting Information). Titrand solutions were prepared by combining 0.833 mL of HCl and the requisite amount of sodium chloride in 500 mL of Milli-Q water. Homopolymers were directly dissolved in this solution at a concentration of 0.2 mg/mL (0.0012 mmol amine/mL). Micelle solutions were prepared by dialyzing micelle stocks against the HCl solution, as described above, and diluted to 0.2 mg amine/mL after dialysis. Carbonatefree NaOH titrant solutions were prepared by dilution of 0.530 mL of 50 wt % NaOH in 500 mL of freshly boiled Milli-Q water. Sodium chloride was added to achieve the requisite total ionic strength. The

solutions were then cooled to room temperature in sealed polyethylene bottles and standardized against potassium hydrogen phthalate (KHP) immediately before use. All titrations were carried out at room temperature (ca. 22−23 °C) using a Titrino 219 S autotitrator (Metrohm) equipped with a doublejunction Ag/AgCl pH electrode (Fisher). Titration curves were analyzed by fitting the derivative of pH with respect to volume to two Gaussian functions to locate the inflection points; the effective pKa was then defined as the pH halfway between these end points. Dynamic Light Scattering. Dynamic light scattering (DLS) measurements were conducted using a Brookhaven Instruments BI200SM light scattering system using a 637 nm laser. Samples were passed through an 0.2 μm filter to remove dust, transferred to glass sample tubes, and placed in the temperature-controlled indexmatching bath, which was held at 23 °C during measurements. Intensity correlation functions from 5 μs to 1 s were acquired at scattering angles from 60° to 120° in 15° increments. Correlation functions were fit to a second-order cumulant expansion, the mutual diffusion coefficient Dm was extracted from a linear fit of the mean decay rate vs q2, and the hydrodynamic radius was finally obtained via the Stokes−Einstein relationship. Viscosities and refractive indices of the buffer solutions were calculated on the basis of equivalent ionic strength sodium chloride solutions.47−50

Figure 1. Schematic illustrating the two-domain equilibrium model used to calculate ion distributions between bulk buffer and PDMAEMA micelle coronas. The equilibria determining the concentrations of these species in each region are described in the text. Equilibrium Model Calculations. Buffer salt distributions were analyzed using a simple two-domain equilibrium model, as illustrated in Figure 1. In this model, the concentrations of H+, OH−, Cl−, Na+, and the buffer species (H2A, HA−, and A2−) in the bulk were set by the required pH, ionic strength, and total buffer salt concentration of the buffer. The concentrations of these species in the corona region, which contained an additional fixed concentration of amine species (R3N and R3NH+), were related to the bulk concentrations via Donnan equilibria.12,31 This model, in which the bulk ion concentrations are fixed and do not change upon interaction with the corona region, was chosen to reflect the equilibration that takes place during dialysis. Concentrations and equilibrium constants were chosen to reflect those in the experimental systems. A summary of all equilibrium, chargebalance, and mass-balance equations included in the model are provided in the Supporting Information.

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RESULTS AND DISCUSSION Micelle Core Sizes and Aggregation Numbers. Representative TEM images of both PDMAEMA-b-PS diblock copolymers and the corresponding core size distributions are shown in Figure 2. Analysis of the TEM images yielded core radii of 16 ± 2 nm for PDMAEMA(18)-b-PS(14) and 9 ± 2 nm PDMAEMA(34)-b-PS(12). Assuming that the density of the polystyrene core is equal to that of bulk polystyrene, these core radii correspond to aggregation numbers of 760 ± 290 and 160 ± 100, respectively. The reported uncertainty in the core 2679

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Figure 2. Representative TEM images of (a) PDMAEMA(18)-b-PS(14) and (c) PDMAEMA(34)-b-PS(12) micelles in acetate buffer at pH 4.5 and 10 mM ionic strength, showing the PS cores. (b, d) Corresponding micelle core size distributions extracted from analysis of TEM images, overlaid with DLS hydrodynamic radius distributions for the same samples in the same pH 4.5, 10 mM ionic strength buffer.

sizes was estimated from the standard deviation of the radius of the micelles in each individual image (typically on the order of 1.5 nm), the variation in the mean core size between different images of the same batch of micelles, and the variation of the calculated radius with choice of thresholding parameter during the image analysis. In Figure 2, the core size distributions extracted from the TEM images are overlaid with the hydrodynamic radius distributions extracted from DLS measurements on the same samples. Both the TEM and DLS data exhibit narrow dispersities (distribution widths less than 10% of the mean), indicating that the cosolvent method produced highly uniform micelles. Titrations and pKa Determination. A typical titration curve for these PDMAEMA-b-PS micelles is shown in Figure 3. In this figure, we have sketched out the end-point analysis used to determine the effective pKa of the sample and overlaid a model titration curve on the data calculated for an ideal monoprotic acid with the same concentration and pKa. The model titration curve agrees well with the experimental data, although it slightly overshoots the experimental curve immediately after each end point. Weak polyelectrolytes, and particularly those in micelle coronas, can exhibit a distribution of pKas,51,52 which may explain this slight mismatch between the experimental titration curve and the curve for the ideal monoprotic acid. However, the overshoot was slightly more prominent at 500 mM and 1 M ionic strengths, suggesting that slow electrode response in the presence of concentrated sodium chloride may also have played a role.

Figure 3. (a) Representative titration curve for PDMAEMA(18)-bPS(14) micelles at 100 mM ionic strength and (b) derivative of the titration curve used to locate titration end points. The derivative in (b) is fit to two Gaussians (red) to locate the inflection points; the effective pKa is then defined as the pH midway between these titration end points. The titration curve in (a) is overlaid with an ideal monoprotic acid titration curve (red) calculated from the parameters extracted from the fit.

The values of the effective pKa extracted from titration curves for each polymer and ionic strength are shown in Figure 4 and tabulated in Table S2. These data reveal several important points about the protonation behavior of PDMAEMA 2680

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Figure 4. Calculated effective pKa values for both sets of PDMAEMA homopolymers and PDMAEMA-b-PS micelles as a function of ionic strength. Values are tabulated in Table S1 (see Supporting Information).

homopolymers and micelle coronas. First, all the measured pKa values are significantly lower than the reported monomer pKa of 8.3,19,29 and the effective pKa of the PDMAEMA homopolymers and micelles increases monotonically toward the monomer pKa with increasing ionic strength. Second, the PDMAEMA-b-PS micelles exhibit pKa values approximately 0.1−0.2 pH units lower than the corresponding homopolymers at high and low ionic strengths, respectively. Third, while the effective pKa appears to be independent of molecular weight for the PDMAEMA homopolymers, there is a small but systematic difference in pKa between the micelles with different PDMAEMA chain lengths in the corona. Finally, to within the accuracy of the fitting and solution concentrations, all amines appear to be titratable in both the homopolymers and micelles at all studied ionic strengths. The convergence of the polymer pKa to the monomer pKa with increasing ionic strength has been observed for PDMAEMA and other weak polyelectrolytes28,51,52 and is attributed to decreasing correlation of the protonation/charge states of nearby monomers as charge screening increases.28 These reported pKa values are roughly consistent with those reported in previous studies of the titration behavior of PDMAEMA,28,29 although direct comparison is difficult since many of these studies were not conducted under constant ionic strength conditions. The discrepancy between the homopolymer and micelle pKas, and the slight difference in the effective pKa of the PDMAEMA(18)-b-PS(14) and PDMAEMA(34)-b-PS(12) micelles, likely results from the higher concentration of amines in the micelle coronas and inability of these species to diffuse into the bulk. Condensation of OH− counterions in the micelle corona raises the corona pH relative to the bulk. As a result, the bulk pH during the deprotonation transition is lower than that in the corona, and the effective pKa (or the bulk pH at which the deprotonation transition occurs) appears to shift to favor the neutral species.12,31 As discussed in the analysis of the DLS data below, the PDMAEMA(18)-b-PS(14) micelles have a higher average concentration of amines in the corona, which leads to a larger shift in their pKa relative to the homopolymers than observed for the PDMAEMA(34)-b-PS(12) micelles. Hydrodynamic Radii. The measured hydrodynamic radii of micelles formed from both PDMAEMA-b-PS polymers in buffers over a range of pH and ionic strengths are shown in Figure 5 and summarized in the Supporting Information (see Table S2). For both polymers, the hydrodynamic radius at fixed

Figure 5. Hydrodynamic radii of (a) PDMAEMA(18)-b-PS(14) and (b) PDMAEMA(34)-b-PS(12) as a function of pH and ionic strength. The error bar represents an estimated uncertainty of ±5% in the hydrodynamic radii obtained by DLS (see Supporting Information).

ionic strength is constant to within the error of the measurements for pH values more than 1 pH unit below the corona pKa but decreases as the ionic strength is increased. As the pH passes the corona pKa, the hydrodynamic radii at all ionic strengths begin to decrease and contract to their minimum values within approximately 2 pH units of the pKa, with the full contraction achieved at a pH closer to the pKa at higher ionic strength. For the highest ionic strength (1 M), the micelles precipitated out above 1 pH unit above the pKa, but for all other ionic strengths the micelles remained soluble at high pH, and the minimum hydrodynamic radius was essentially independent of the ionic strength. The minimum radii predicted by the aggregation numbers calculated from the TEM images are 20 ± 3 nm for PDMAMEA(18)-b-PS(14) and 13 ± 3 nm for PDMAEMA(34)-b-PS(12), compared to average values of approximately 25 and 22 nm observed by DLS, indicating that the corona is still somewhat swollen even in its minimally extended state. On the other hand, comparing the contour lengths of the PDMAEMA blocks (29 nm for PDMAEMA(18)-b-PS(14) and 54 nm for PDMAEMA(34)-bPS(12)) to the maximum corona extension (approximately 23 and 38 nm, respectively) reveals that at low ionic strength the coronas in the PDMAEMA(18)-b-PS(14) micelles are almost fully extended, while those in the PDMAEMA(34)-b-PS(12) micelles may be somewhat more relaxed. Because the polystyrene cores of the micelles are frozen in aqueous solution,46 the changes in the hydrodynamic radius at different pH and ionic strength result solely from changes in the corona conformation. Qualitatively, the corona behavior is consistent with that predicted for salted osmotic brushes and reported for similar experimental systems, in which either increasing the ionic strength or decreasing the corona charge density reduces the osmotic pressure driving corona extension 2681

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studies on other polyelectrolyte systems typically also report weaker scaling than predicted, with exponents from −0.11 to −0.20 reported for starlike micelles.13−15,17 Theoretical work has attributed these discrepancies to excluded volume effects; incorporating the electrostatic excluded volume into models for spherical polyelectrolyte brushes, for example, reduces the expected scaling to as low as cs−1/10 in the salt-dominated regime for spherical polyelectrolyte brushes with infinitely small cores.14 Thus, being in the crossover region between the starlike and planar-like brush limits, not being fully in the saltdominated regime, and excluded volume effects likely all contribute to the observed scaling of the micelle radius and corona extension with increasing ionic strength. The observation that the full contraction is achieved at a pH closer to the pKa at higher ionic strength may reflect the criterion that corona contraction begins when the osmotic pressure inside the brush is equivalent to that of the bulk, near cs = ci. At lower ionic strength, a larger fraction of the corona chains must be deprotonated to reduce the corona counterion concentration to that of the bulk, thus requiring a higher pH to initiate contraction. However, this explanation would suggest that the ionic strength dependence should be different for micelles with different intrinsic counterion concentrations in the corona, and we do not see a significant difference in the pHdependent contraction between PDMAEMA(18)-b-PS(14) and PDMAEMA(34)-b-PS(12) micelles, so the data are not conclusive on this point. Figures 5 and 6 include only data for micelles in monoprotic buffer solutions, which are consistent with previous reports on charge-annealed polyelectrolyte micelles in unbuffered solutions. In polyprotic buffers, however, we anticipate that the corona behavior may be significantly more complex, as buffer anions accumulate in the corona and skew the buffer equilibrium toward multivalent species, which are known to cause contraction of polyelectrolyte brushes. In the next section, we describe equilibrium models and experimental data that provide evidence for this polyprotic buffer effect. Buffer Equilibrium Calculations. Calculated ion distributions using the two-domain equilibrium model described previously are shown in Figure 7. In these calculations, the total concentration of buffer salt in region I (“bulk”) was set to 20 mM and the pH was set equal to the pKa,1 of the buffer (pKa,1 = 3), yielding 10 mM ionic strength in the absence of added salt. In Figures 7a,b, the total amine concentration in region II (“corona”) was set to 100 mM. As shown in Figure 7a, when no additional salt is added to the buffer, the ratio of divalent buffer anions (A2−) to monovalent buffer anions (A−) in region II increases by a factor of up to 2.5 relative to region I, indicating that concentration of buffer anions in the micelle corona can indeed skew the buffer equilibrium toward production of divalent species. While Donnan equilibrium leads to accumulation of divalent species in the corona region in any solution with a fixed concentration of divalent anions (see Supporting Information), shifts in the buffer equilibrium provide a more useful conceptual framework in the current system since the divalent ion concentration is directly controlled byand may change withthe solution pH. This skewed buffer equilibrium results in a significant fraction of all countercharges in the micelle corona being contributed by divalent species, as shown in Figure 7b, which should result in corona contraction in experimental systems. This effect is most pronounced when the pKa,2 of the buffer is close to the pH at which the buffer is used and when there is little added salt in

Figure 6. (a) Hydrodynamic radii and (b) corona extension of PDMAEMA-b-PS micelles at pH 4.5 as a function of ionic strength. Scaling exponents calculated from the slope of linear fits to the data on a log−log scale are indicated.

and results in a decrease in the micelle size.12,16 To investigate the pH and ionic strength effects more quantitatively, we examine the scaling of the hydrodynamic radius and corona extension as a function of salt concentration, as shown in Figure 6. For the PDMAEMA(18)-b-PS(14) micelles, the hydrodynamic radius scales as cs−0.05±0.01. The corona extension, defined as Lcorona = Rh − Rcore, scales as cs−0.10±0.04, where cs is the total ionic strength resulting from buffer species and added salt. For the PDMAEMA(34)-b-PS(12) micelles, the magnitude of the scaling exponent is somewhat larger, at −0.09 ± 0.01 for the hydrodynamic radius and −0.13 ± 0.03 for the corona extension. While the uncertainties in the corona extension are slightly larger than those of the hydrodynamic radii because of the additional uncertainty in the core size extracted from TEM, the scaling exponents are sufficiently well-defined to allow comparison with theoretical predictions. Interestingly, even after taking the uncertainty in the corona extension into account, the calculated exponents are all smaller than those predicted by mean-field descriptions of polyelectrolyte micelles. These models assert that the radius of starlike micelles should scale with salt concentration as cs−1/5, while the coronas of crew-cut micelles should, like planar polyelectrolyte brushes, scale as cs−1/3.12,53 However, these predictions assume that the brushes are completely in the salt-dominated regime, in which the intrinsic counterion concentration ci is much smaller than the bulk solution salt concentration (that is, cs ≫ ci), a criterion that may not be met for these micelle coronas. We calculate, for example, average monomer concentrations of 0.6 ± 0.3 and 0.13 ± 0.09 M for PDMAEMA(18)-b-PS(14) and PDMAEMA(34)-b-PS(12) micelles, respectively, when the corona is in its fully extended state at 10 mM ionic strength, but the real concentration could be significantly higher near the core and lower near the edge of the corona. Experimental 2682

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equilibrium leads to an increase in the fraction of counterion charges contributed by divalent species. In experimental systems, this buildup of divalent species should correspond to more pronounced corona contraction due to buffer effects in micelles with a higher intrinsic amine concentration in the corona. These predictions were tested by measuring hydrodynamic radii of micelles dialyzed into polyprotic buffers at constant pH but with different second dissociation constants. In Figure 8, we

Figure 8. Hydrodynamic radii of (a) PDMAEMA(18)-b-PS(14) and (b) PDMAEMA(34)-b-PS(12) micelles in polyprotic buffers at pH 3 (vertical dashed line). Hydrodynamic radii (Rh) are plotted as a function of the negative log of the second acid dissociation constant (pKa,2) of the polyprotic buffers. Increasing pKa,2 indicates decreasing propensity for singly charged buffer species to dissociate into divalent species; monoprotic and unbuffered solutions are plotted to the right to indicate the limit of no dissociation into divalent species. A complete list of buffers and measured hydrodynamic radii is given in the Supporting Information (Table S4).

Figure 7. (a) Calculated ratio between divalent and monovalent buffer anions and (b) resulting fraction of corona anion charges contributed by divalent species for 20 mM buffer used at its pKa,1 and [R3N]c,tot = 100 mM. (c) Fraction of corona anion charges contributed by divalent species for 20 mM buffer used at its pKa,1 with 0 mM added salt.

the system. When the system contains 990 mM of added monovalent salt, on the other hand, the buffer equilibrium in the micelle corona is nearly indistinguishable from that in the bulk; the fraction of anion charges contributed by divalent species correspondingly drops nearly to 0, both because there is less buildup of buffer anions in the corona and thus a less dramatic shift in the buffer equilibrium, and because buffer species make up a smaller overall fraction of the anions in the solution. As the salt concentration is increased, the corona behavior in polyprotic buffers should thus become indistinguishable from that in monoprotic or unbuffered solutions at the same ionic strength. In Figure 7c, the total concentration of buffer salt in region I is again set equal to 20 mM, and it is again used at its pKa,1. This time, however, the concentration of added salt is held constant at 0 mM, and the total concentration of amines in region II is varied. As the concentration of amines in region II increases, the charged buffer species become more concentrated in this region, and the resulting shift in the buffer

report the hydrodynamic radii of PDMAEMA-b-PS micelles dialyzed into several different polyprotic buffers. As shown in this figure, the polyprotic buffers used in this experiment cause significant contraction of the micelle corona relative to monoprotic buffers and unbuffered solutions, even though all solutions were prepared at the same pH, and the degree of contraction depends on the pKa,2 of the buffer relative to the pH, as predicted by the equilibrium model. Micelles dialyzed into phosphate buffer (which has a large pKa,2) have a hydrodynamic radius that matches that of micelles in monoprotic buffer (formate) and unbuffered (HCl) solutions, indicating (as the model suggests) that there is no significant accumulation of divalent anions in the micelle corona that would lead to corona contraction. On the other hand, the model predicts that at pKa,2 − pH = 1.5 and 10 mM ionic strength, between 30 and 70% of the counterion charges in the corona may be contributed by divalent buffer species, depending on the amine concentration in the corona. Micelles 2683

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micelles with a higher effective concentration of amines in the corona. We make three further observations about the polyprotic buffer effect in spherical polyelectrolyte brushes and micelles. First, while the model only explicitly describes diprotic buffers, a similar argument could be made for triprotic and polyprotic systems. In fact, two of the buffers used in these experiments (citrate and phosphate) are triprotic buffers. For phosphate pKa,3 is large (approximately 12.4) and unlikely to further skew the buffer equilibrium in the brush toward trivalent species, but for citrate pKa,3 is much smaller (approximately 6.4). This could potentially explain why the Rh observed for micelles in citrate was slightly smaller than for those in fumarate buffer despite their similar pKa,2s, although the discrepancy is small enough (and within the experimental error) that it is hard to draw any conclusions based on this observation. Second, the polyprotic buffer effect reported here is likely much more important for cationic polyelectrolyte brushes than anionic brushes. Polyelectrolyte brushes are only expected to exhibit significant contraction in the presence of oppositely charged multivalent counterions, but not in the presence of like-charged multivalent co-ions.41 While polyanionic brushes should exhibit similar anomalous contraction in the presence of multiply charged cationic buffers, most common polyprotic organic buffers involve equilibria between a neutral species and anionic charged species rather than between a neutral species and cationic charged species. However, equilibrium shifts may still be observed when anionic polyelectrolyte brushes are in equilibrium with short polypeptides or redox systems involving multiple cationic states. Finally, particularly for biological applications, phosphate buffer has a large enough pKa difference and is present at low enough concentrations (ca. 1 mM) that it is unlikely to undergo significant equilibrium shifts upon accumulation in polyelectrolyte brushes and micelle coronas, though it is already in equilibrium with its divalent form at physiological pH. Carbonate buffer, on the other hand, has a pKa,2 approximately 3 pH units above physiological pH and is present at approximately 24 mM concentrations.38 At physiological ionic strength (ca. 154 mM), the accumulation of bicarbonate anions in a polyelectrolyte brush or micelle corona and the corresponding equilibrium shift is likely to be small but may still lead to measurable effects in brushes with a high average monomer concentration.

dialyzed into fumarate and citrate buffers correspondingly exhibit significant contraction relative to the monoprotic and unbuffered samples. Micelles in malonate buffer, which is a dicarboxylic acid but has a larger pKa,2 than either fumaric or citric acid, do not contract as much as those in fumarate or citrate buffers, indicating that the contraction in fumarate and citrate buffers cannot be attributed simply to specific interactions (e.g., hydrogen bonding) between the corona amines and the buffer carboxylate groups. Last but not least, micelles dialyzed into sulfate buffer, which has a pKa,2 of 1.99 and should be dominated by divalent anions even in the bulk solution at pH 3, exhibit even more marked contraction. While this case, in which both the pKa,1 and the pKa,2 are significantly below the solution pH, is not included in Figure 7, it provides a convenient reference for the extent of contraction when divalent anions dominate. In Figure 8, we also show data for micelles in the same buffers but with a total ionic strength of 100 mM rather than 10 mM. We see that while the micelles still contract when pKa,2 is close to or below the solution pH, the dependence on the pKa,2 is much weaker, as predicted by the model. The salt dependence is explored in more detail in Figure 9, in which

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CONCLUSIONS In summary, we have demonstrated that cationic spherical polyelectrolyte brushes with PS cores and PDMAEMA coronas exhibit behavior consistent with previous studies on salted polyelectrolyte brushes when investigated in monoprotic buffer solutions. In polyprotic buffers, however, the brush behavior is significantly more complex. When the dissociation constants of the buffer are close, accumulation of charged buffer species in the micelle corona without the corresponding neutral species can skew the buffer equilibrium toward divalent species, leading to anomalous corona contraction. This result is of particular importance because many applications of polyelectrolyte brushes are in buffered systems, and researchers studying polyelectrolyte brushes and their applications should keep potential buffer effects in mind when designing their experimental systems.

Figure 9. Comparison of hydrodynamic radii of (a) PDMAEMA(18)b-PS(14) and (b) PDMAEMA(34)-b-PS(12) in monoprotic buffer (formate) and triprotic buffer (citrate) at low pH and 10 mM total ionic strength. Micelles in citrate buffer exhibit significant contraction relative to those in formate buffer at similar charge density.

we compare micelles in citrate and formate buffers close to their pKas. For the PDMAEMA(34)-b-PS(12) micelles, the hydrodynamic radii are nearly identical at ionic strengths of 100 mM and above. For the PDMAEMA(18)-b-PS(14) micelles, small differences persist to ionic strengths of at least 250 mM. While these differences are within the uncertainty of the DLS measurements, this result is consistent with the prediction that the shift in the buffer equilibrium and the corresponding contraction of the micelles should be more pronounced in 2684

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ASSOCIATED CONTENT

S Supporting Information *

Figures S1−S4, Tables S1−S4, and eqs S1−S22. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (T.P.L.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank Ron Siegel for loan of equipment. This work was funded primarily by the National Science Foundation through the University of Minnesota Materials Research Science and Engineering Center (DMR-1420013 and 0819885). Parts of this work were carried out in the College of Science & Engineering Characterization Facility, University of Minnesota, which receives partial support from NSF through the MRSEC program. J.E.L. is supported in part by the L’Oréal For Women in Science Postdoctoral Fellowship program.

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