Equilibration of Micelle–Polyelectrolyte Complexes - ACS Publications

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Equilibration of Micelle−Polyelectrolyte Complexes: Mechanistic Differences between Static and Annealed Charge Distributions Jennifer E. Laaser,† Michael McGovern,‡ Yaming Jiang,‡ Elise Lohmann,† Theresa M. Reineke,† David C. Morse,‡ Kevin D. Dorfman,‡ and Timothy P. Lodge*,†,‡ †

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

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S Supporting Information *

ABSTRACT: The role of charge density and charge annealing in polyelectrolyte complexation was investigated through systematic comparison of two micelle−polyelectrolyte systems. First, poly(dimethylaminoethyl methacrylate)-block-poly(styrene) (PDMAEMA-b-PS) micelles were complexed with poly(styrenesulfonate) (PSS) at pH values above and below the pKa of PDMAEMA to investigate the role of charge annealing in the complexation process. Second, complexes of poly(DMAEMA-stat-oligo(ethylene glycol) methyl ether methacrylate)-block-poly(styrene) (P(DMAEMA-statOEGMA)-b-PS) micelles with the same PSS at low pH were used to investigate how the complexation process differs when the charged sites are in fixed positions along the polymer chains. Characterization by turbidimetric titration, dynamic light scattering, and cryogenic transmission electron microscopy reveals that whether or not the charge distribution can rearrange during the complexation process significantly affects the structure and stability of the complexes. In complexes of PDMAEMA-b-PS micelles at elevated pH, in which the charge distributions can anneal, the charge sites redistribute along the corona chains upon complexation to favor more fully ion-paired configurations. This promotes rapid rearrangement to single-micelle species when the micelles are in excess but traps complexes formed with PSS in excess. In complexes with static charge distributions introduced by copolymerization of DMAEMA with neutral OEGMA monomers, on the other hand, the opposite is true: in this case, reducing the charge density promotes rearrangement to singlemicelle complexes only when the polyanion is in excess. Molecular dynamics simulations show that disruption of the charge density in the corona brush reduces the barrier to rearrangement of individual ion pairs, suggesting that the inability of the brush to rearrange to form fully ion-paired complexes fundamentally alters the kinetics of complex formation and equilibration.

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INTRODUCTION Controlling the structure and dynamics of polyelectrolyte complexes and coacervates is an important requirement for emerging applications of these materials in fields as diverse as drug and nucleic acid delivery,1−4 wastewater treatment,5,6 selfhealing materials,7 and hydrogel networks.8,9 A critical limitation in many of these applications, however, is that mixtures of oppositely charged polyelectrolytes typically form kinetically trapped complexes that rearrange on slow time scales (hours, days, or weeks) toward their thermodynamically favored structures.10−12 While elevated temperature and high ionic strength can in many cases be used to promote equilibration of polyelectrolyte complexes and coacervates,7,13 these approaches add additional processing steps and are not compatible with all applications. Developing polymer design strategies that use the structure of the polymer itself to reduce kinetic trapping and promote rapid equilibration could dramatically improve the versatility and viability of polyelectrolyte complexes as a platform for diverse applications. Tuning the charge density of one or both of the polyelectrolyte species is a promising route for controlling © 2017 American Chemical Society

both the structure and equilibration kinetics of polyelectrolyte complex materials and tailoring their properties for specific applications.14,15 Experiments on polyelectrolyte complexes and coacervates, for example, typically show a change in the complex structure, composition, or stoichiometry when the charge density of one of the polyelectrolyte components is reduced by copolymerization of charged moieties with neutral, uncharged monomers.16−20 In polyelectrolyte multilayers, there is typically a critical charge density below which multilayers cannot form,21−23 and similar effects are observed when one component is a weak polyelectrolyte and the charge density is reduced by changing pH rather than by permanent introduction of uncharged sites.24,25 While these effects reflect changes in the structure and composition of the complexes, other work suggests that changes in charge density should affect the equilibration and rearrangement kinetics in polyelectrolyte complex materials as well.26,27 Rheological measurements on Received: February 28, 2017 Revised: April 13, 2017 Published: April 25, 2017 4631

DOI: 10.1021/acs.jpcb.7b01953 J. Phys. Chem. B 2017, 121, 4631−4641

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The Journal of Physical Chemistry B Scheme 1. Synthesis of (D/O)S(27-13) Polymers by RAFT Polymerization

favorable configuration. In the second case, the micelles are assembled from poly(dimethylaminoethyl methacrylate-statoligo(ethylene glycol) methyl ether methacrylate)-block-poly(styrene) ((D/O)S) polymers. In these micelles, the coronas have static charge distributions at low pH that are unable to anneal because they contain neutral, hydrophilic monomers randomly placed at fixed locations within the corona chains. The complexation of these micelles with PSS is investigated via turbidimetric titration, dynamic light scattering, ζ-potential, and cryogenic transmission electron microscopy. These experiments reveal that reducing the charge density in micelles, either by increasing pH or introducing neutral monomers, generally accelerates the rearrangement kinetics of the micelle− polyelectrolyte complexes. However, the static or dynamic nature of the charge distribution affects the structures toward which they rearrange. To gain further insight into the origin of this difference, we use molecular dynamics simulations, which reveal how insertion of uncharged monomers at fixed points in the micelle corona promotes overcharging and rearrangement of the polyelectrolyte complexes. Together, these experiments and simulations provide new insight into how different methods of manipulating polymer charge density can be used to control the structure and stability of polyelectrolyte complexes.

complex coacervates, for example, show that reducing the charge density by changing pH reduces the overall strength of interactions between chains and accelerates relaxation in the material.27−29 Single-molecule force measurements also indicate that the lifetime of just four or five adjacent ionic bonds may be many orders of magnitude longer than those of single ionic bonds under the same conditions,26 which should result in slower rearrangement kinetics at higher charge densities. While significant evidence indicates that charge density could be a viable means to control both the structure and equilibration kinetics of polyelectrolyte complexes, fundamental questions still remain. First, it is often implicitly assumed that reducing the charge density by changing pH is equivalent to reducing the charge density by copolymerizing with neutral, uncharged units.25,27 However, this may not be true, since charge annealing in weak polyelectrolytes may provide equilibration pathways not accessible to polyelectrolytes with fixed charge distributions.30,31 Second, because most studies investigating the role of charge density in polyelectrolyte complexation have focused on its effects on the structure, composition, and overall stability of the materials, significant work remains to be done to understand how charge density controls equilibration and rearrangement kinetics. In this work, we use cationic polyelectrolyte micelles as a platform for investigating the role of charge density in determining the structure and equilibration kinetics of complexes with polyanions. Polyelectrolyte micelles are a promising platform because the micelles and their complexes are amenable to a wide range of solution characterization techniques,12,32−38 and the micelles can be designed for direct comparison of pH- and copolymerization-induced changes in charge density. We utilize two polyelectrolyte micelle systems for this task. In both micelle systems, the charged sites in the micelle coronas consist of protonated tertiary amines, and the micelles are complexed with linear poly(styrenesulfonate) (PSS). However, the charge density in the micelle corona is controlled in two different ways. In the first, the micelles are self-assembled from poly(dimethylaminoethyl methacrylate)block-poly(styrene) (DS) block copolymers. These polymers form micelles with hydrophobic poly(styrene) (S) cores and hydrophilic, protonatable poly(dimethylaminoethyl methacrylate) (D or D+) coronas.39 These micelles have “annealed” charge distributions in which the charge density can be adjusted by changing the solution pH, and the number and location of charged sites within the corona can also rearrange during and after complexation to reach the most thermodynamically

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MATERIALS AND METHODS Materials. N,N-Dimethylaminoethyl methacrylate (DMAEMA), oligo(ethylene glycol) methyl ether methacrylate (OEGMA, Mn = 500 g/mol), styrene, 4,4′-azobis(4-cyanovaleric acid) (ACVA), azobis(isobutyronitrile) (AIBN), and 4cyano-4-[(dodecylsulfanylthiocarbonyl)sulfanyl]pentanoic acid (CDTPA) were purchased from Sigma-Aldrich. All monomers (DMAEMA, OEGMA, and styrene) were filtered through activated neutral alumina immediately before use to remove inhibitors, and AIBN was recrystallized from methanol. Toluene, methanol, hexanes, glacial acetic acid, sodium chloride, and buffer salts 2-(N-morpholino)ethanesulfonic acid (MES), 4-(2-hydroxyethyl)-1-piperazineethanesulfonic acid (HEPES), and tris(hydroxymethyl)aminomethane (TRIS) were purchased from both Sigma-Aldrich and Fisher Scientific and used as received. Poly(styrenesulfonate) (PSS) with a molecular weight of 29 kg/mol (PSS-30) was purchased from Polymer Standards Service (Mainz, Germany) with a quoted dispersity of less than 1.2 and degree of sulfonation greater than 95%. Regenerated cellulose dialysis tubing with an 8 kg/mol cutoff was purchased from Spectrum Laboratories. 4632

DOI: 10.1021/acs.jpcb.7b01953 J. Phys. Chem. B 2017, 121, 4631−4641

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The Journal of Physical Chemistry B

starting polyelectrolyte solution was placed in a vial, and 50 μL aliquots of a solution of the oppositely charged polyelectrolyte were added dropwise while monitoring the transmission of a 632 nm HeNe laser on a Spex Industries laser power meter. Small portions (0.500 mL) of the titration solution were removed after every 10 additions to facilitate reaching higher charge ratios with small samples, and the sample heterogeneity was assessed visually throughout the course of the titration. Dynamic Light Scattering. Dynamic light scattering experiments were carried out on a Brookhaven Instruments BI-200SM scanning multiangle light scattering instrument equipped with a 637 nm diode laser and an avalanche photodiode detector. Samples were prepared using a titration technique similar to that described above, with all solutions filtered through 200 nm filters before titration and all vials, stir bars, and sample tubes rinsed four times with filtered solvent to remove dust before use. Scattered intensity autocorrelation functions were obtained at room temperature (23 °C) at a scattering angle of 90° over time delays from 1 μs to 1 s and were averaged for 30 min at a count rate of approximately 300 kilocounts/s. Decay time distributions were acquired by an inverse Laplace transform of the intensity autocorrelation functions using the REPES algorithm with a probability to reject of 0.5,41 and decay times were finally converted to hydrodynamic radii via the Stokes−Einstein relationship, using viscosities and refractive indices for equivalent ionic strength sodium chloride solutions. Peak positions were also extracted by fitting the hydrodynamic radius distributions to a sum of lognormal distributions. ζ-Potentials. The ζ-potentials were measured using a Zetasizer Nano ZS (Malvern Instruments). Samples for ζpotential measurements were prepared under the same conditions as those used for DLS and were transferred to a disposable folded capillary cell for measurement. Electrophoretic mobilities were measured using the Malvern M3-PALS method and converted to ζ-potentials by the Smoluchowski equation. The reported values were taken from the average of three measurements. Samples typically had conductivities around 1 mS/cm. Cryogenic Transmission Electron Microscopy. Samples for cryogenic transmission electron microscopy (cryoTEM) were vitrified on a FEI Vitrobot Mark III vitrification robot. For each sample, approximately 3.3 μL of solution was pipetted onto a lacey carbon−Formvar coated copper TEM grid (300 mesh, Ted Pella). The grid was then blotted for 5 s and drained for 1 s before being vitrified by plunging into liquid ethane (90 K). Samples were stored under liquid nitrogen before use and transferred to a single-tilt cryo holder for imaging. TEM images were acquired on a FEI Technai G2 Spirit BioTWIN electron microscope operating at an accelerating voltage of 120 kV and imaged on an Eagle 4 megapixel CCD camera. Images were acquired at a slight underfocus for adequate contrast. Molecular Dynamics Simulations. Molecular dynamics simulations were carried out on a simple model system consisting of a cationic polymer brush in contact with a solution containing anionic homopolymers and monovalent small ions. Polymer chains were simulated as bead−spring chains with one bead per monomer. The solvent was treated implicitly as a uniform dielectric medium. Simulations were conducted using the LAMMPS simulation package,42 using a Langevin dynamics integrator with a damping factor of 7 in Lennard-Jones time units. The cationic polymer brush consisted of polymer chains tethered to a wall on one end. The terminal monomer of each

Polymer Synthesis. Synthesis of the DS(30-8) polymer (containing a 30 kg/mol DMAEMA block and an 8 kg/mol S block) was reported previously.38 The (D/O)S(27-13) polymer was synthesized via a similar two-step RAFT polymerization process, as shown in Scheme 1. First, the (D/O)-27 macrochain transfer agent (macro-CTA) was synthesized from a commercially available chain transfer agent and initiator. CDTPA (96.9 mg, 0.24 mmol), ACVA (6.9 mg, 0.02 mmol), DMAEMA (6.08 g, 0.039 mol), and OEGMA (6.03 g, 0.012 mol) were combined with 18.35 g of toluene in a Schlenk flask. The reaction mixture was degassed via three freeze−pump− thaw cycles before being stirred at 80 °C for 4.5 h. Aliquots were withdrawn at regular intervals to monitor the reaction progress and monomer conversion. After the reaction was complete, the mixture was cooled to room temperature, diluted 2-fold with methanol, and dialyzed against four changes of methanol to remove unreacted monomer. Solvent was removed from the dialyzed polymer solution by rotary evaporation and drying under vacuum overnight, yielding the (D/O)-27 macroCTA as a viscous yellow liquid. The macroinitiator was characterized by 1H NMR spectroscopy on a Bruker HD-500 spectrometer equipped with a cryoprobe. It was also characterized by size exclusion chromatography (SEC) in THF eluent with 1% added tetramethylethylenediamine on an instrument equipped with multiangle light scattering and refractive index detectors (Wyatt Technology). NMR: wDMAEMA = 0.53, wOEGMA = 0.47; SEC: Mn = 27 kg/mol, Đ = 1.12. Full characterization data and verification of the near-random nature of the statistical copolymerization are provided in the Supporting Information (Figures S1 and S2).40 The (D/O)S(27-13) block polymer was then synthesized by chain extension of the (D/O)-27 macro-CTA. (D/O)-27 (2.62 g, 0.097 mmol), AIBN (0.8 mg, 0.005 mmol), and styrene (10.90 g, 0.053 mol) were dissolved in 10.94 g of toluene, degassed via three freeze−pump−thaw cycles, and polymerized at 80 °C for 24 h. The reaction mixture was cooled to room temperature and quenched by exposure to the atmosphere. The polymer was then precipitated twice from hexanes and freezedried from benzene, yielding the (D/O)S(27-13) block polymer as a spongy yellow solid. NMR: Mn = 40 kg/mol; SEC: Mn = 41 kg/mol, Đ = 1.10. NMR and SEC traces of the (D/O)-27 macro-CTA and (D/O)S(27-13) block polymer are provided in Figures S3 and S4, and the characterization data are summarized in Table S1. Micelle Formation. Micelles were formed by a cosolvent addition method, as described previously.39 Briefly, the DS(308) and (D/O)S(27-13) block polymers were each dissolved in dimethylformamide at a concentration of 10 mg/mL. An equal volume of 100 mM TRIS buffer at pH 7.25 was added dropwise, after which the solutions were further diluted 2-fold, dialyzed against four changes of the desired aqueous buffer, and diluted with excess dialysate to a final concentration of approximately 1.2 mM amine. PSS solutions were prepared at a concentration of 1.2 mM sulfonate groups by direct dissolution of dry PSS samples in excess buffer from dialysis. The buffers used in this work were 20 mM acetate, 14 mM MES, 20 mM HEPES, and 20 mM TRIS at pH 4.5, 6.5, 7.5, and 8.5, respectively, with a total ionic strength of 10 mM set by addition of sodium chloride. All buffers were prepared from Milli-Q water with a reported resistivity of 18.2 MΩ. Turbidimetric Titrations. Turbidimetric titrations were carried out on a home-built light transmission apparatus as described previously.12 Briefly, a 1.250 mL aliquot of the 4633

DOI: 10.1021/acs.jpcb.7b01953 J. Phys. Chem. B 2017, 121, 4631−4641

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The Journal of Physical Chemistry B tethered chain was free to move in the x and y directions but was constrained to a plane of constant z = 0. The system was a periodic box in the x and y directions but was finite in the z dimension. All particles were constrained to remain within the box by repulsive 12−6 wall potentials at the two extremes of z, denoted by z = 0 and z = Lz. To minimize artifacts associated with the wall, a linker region of 10 neutral monomers, including the monomer constrained at the wall, was included in all of the brush polymers. The brush consisted of 64 cationic copolymer chains, each of which had 30 positive monovalent monomers and 40 neutral monomers, including the 10 linker monomers, as shown subsequently in Figure 6. The monomers were either arranged in two blocks, one with 40 neutral monomers and the other with 30 positive monomers (“block” case), or with one block of 10 neutral monomers (the linker) and an alternating series of 30 positive and 30 neutral monomers (“alternating” case). Results were calculated for varying numbers of 0−200 polyanion homopolymer chains. Each of these polyanion chains consisted of 30 negatively charged monomers. For each charged monomer in either the brush or the free polyanions, a monovalent counterion was present. A total of 705 additional monovalent ions of each type were also added to approximate 10 mM salt. Adjacent monomers in the polymer chains were bound by a FENE potential with K = 30, R0 = 1.6, ε = 1.5, and σ = 1. All monomers and free counterions interacted through a purely repulsive Weeks−Chandler−Andersen (WCA) potential with a common Lennard-Jones ε equal to the thermal energy kBT, and the same Lennard-Jones diameter for all particle types, in addition to electrostatic interactions. All parameters aside from charge were identical for all of the monomers and counterions in the simulation. The dielectric constant was chosen to give a Bjerrum length equal to 3σ to match the ratio of Bjerrum length to monomer spacing in the experimental system. The dimensions of the simulation cell in the x, y, and z directions were 120 × 120 × 120 in units of the WCA Lennard-Jones diameter σ. Electrostatic interactions were calculated using a particle−particle Ewald summation with a maximum error of 10−5. A slab geometry was used to allow the use of Ewald methods (which require a periodic unit cell) to simulate a unit cell that was effectively nonperiodic in the z direction by inserting an empty space along the z dimension such that the length of the periodic unit cell in the z dimension was 3.0 times larger than the length Lz of the region to which all particles were confined. For each polyanion:polycation ratio, the simulations were analyzed by calculating the concentration of free polyanions, the electrostatic energy, and the average lifetime of contacts between oppositely charged polyion monomers. Two oppositely charged polyion chains were considered to be in contact if at least one monomer pair was within two monomer radii; the contact lifetime was defined as the duration of the contact. The number of free polyanions was defined as the number of polyanions with no contacts with polycation chains.

Figure 1. Regions of colloidal instability for complexes of DS(30-8) micelles with PSS-30 in buffers at 10 mM ionic strength with different pH. In (a), the regions of colloidal instability are plotted against the ratio of sulfonate units to amine units in the sample, while in (b) and (c), they are plotted against the charge ratio, calculated using only the fraction of DMAEMA units which would be charged if the pKa of the PDMAEMA corona were (b) pH 6.5 and (c) pH 8, as described in the Supporting Information. The pKa of PDMAEMA at 10 mM ionic strength is approximately 6.5.

conditions where the PDMAEMA block is expected to range from almost fully protonated (pH 4.5) to partially deprotonated (pH 6.5 and 7.5) and almost fully deprotonated (pH 8.5). As is evident in Figure S5, the overall shape of the titration curves was relatively similar across the entire pH range, with both the forward and reverse titrations exhibiting a slow decrease followed by a rapid drop in the transmission concurrent with the onset of macroscopic phase separation. However, the region of colloidal instability, defined as the range of [sulfonate]/[amine] values between the forward and reverse titration end points at which the solution transmission dropped below 85%, shifted to lower [sulfonate]/[amine] ratios with increasing pH. The regions of colloidal instability shown in Figure 1a are plotted as a function of [sulfonate]/[amine], or the number of sulfonates per amine group in the mixture. At pH 4.5, when the tertiary amines in the DMAEMA side chains are almost 100% protonated, [sulfonate]/[amine] directly reflects the charge ratio, and the stoichiometric charge ratio occurs at [sulfonate]/ [amine] = 1. This coincides with the region of colloidal instability, which reflects the instability of the micelle− polyelectrolyte complexes near charge neutrality. At higher pH, deprotonation of the amine side chains means that a lower [sulfonate]/[amine] ratio should be required to achieve charge neutrality, an expectation that is indeed qualitatively consistent with the shift in the regions of colloidal instability in Figure 1a. Rescaling the x-axis to reflect the expected charge ratio at each pH (Figure 1c and Supporting Information) should yield

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RESULTS Complexes of Micelles with Annealed Charge Distributions. Turbidimetric titration data for DS(30-8) micelles with PSS-30 at 10 mM ionic strength and varying pH are presented in Figure S5 and summarized in Figure 1. Because the pKa of PDMAEMA in micelle coronas is approximately 6.5 at 10 mM ionic strength,31,39,43−45 this pH range covers 4634

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Figure 2. Hydrodynamic radius distributions of complexes of DS(30-8) micelles with PSS-30 in (a) MES buffer at pH 6.5 and (b) HEPES buffer at pH 7.5, both at a total ionic strength of 10 mM. Samples were prepared at [−]/[+] values of 2.45 (excess PSS) and 0.41 (excess micelles).

this bimodal size distribution was attributed to a kinetically trapped mixture of single micelle complexes and multimicelle aggregates.12 At pH 7.5, the complexes again exhibited bimodal size distributions immediately after formation. While this distribution remained stable for complexes formed with an excess of PSS, those formed with an excess of the cationic micelles were no longer kinetically trapped and rearranged to a monomodal distribution of particles slightly smaller than the uncomplexed micelles in under 1 week. As discussed in more detail below, this result suggests that complexes with an excess of annealable cations have the ability to rearrange to more favorable configurations by rearranging their charge distribution and ion pairing, while those with an excess of polyanion have most cation sites paired from the start and do not have enough free sites to facilitate the rearrangement process. Complexes of Micelles with Fixed Charge Distributions. Turbidimetric titration data for complexes of (D/ O)S(27-13) micelles with PSS-30 at low pH and ionic strength are presented in Figure 3. At pH 4.5, the DMAEMA units are nearly all protonated, and the statistical distribution of the charged DMAEMA and neutral OEGMA monomers thus leads to a statistical distribution of charges along the corona chains. With approximately three charged DMAEMA monomers for every neutral OEGMA monomer, the charge density of (D/ O)S(27-13) micelles at pH 4.5 is similar to that of the DS(308) micelles at pH 6. As shown in Figure 3, the titration curves were similar to those for micelles containing only DMAEMA in the coronas. As in those systems, the region of colloidal instability was centered around [sulfonate]/[amine] = 1, indicating that disruption of the corona charge density by inclusion of bulky neutral hydrophilic units does not significantly affect the stoichiometry of the complexation process. Additionally, in both systems, the mismatch between the forward and reverse titration curves suggests that the complexes are kinetically trapped on the time scale of the titration measurement, as has been observed previously.12 On the basis of the turbidimetric titration measurements, static dilution of the charge density by copolymerization with a neutral monomer appears to have little effect on the complexation process. DLS measurements, however, reveal unexpected behavior in the week-long rearrangement kinetics. As in the systems containing DMAEMA-only coronas, the mixtures initially formed complexes with bimodal size distributions, as shown in Figure 4. This time, however,

regions of colloidal instability centered around the charge neutral point at [−]/[+] = 1. Performing this analysis with a pKa of 6.5, however, yields regions of colloidal instability that instead shift to [−]/[+] values far above the charge neutral point at high pH. Further analysis suggests that this result is consistent with previously observed shifts in the average pKa of weak polyelectrolytes upon complexation with an oppositely charged polymer.31 Performing the same analysis, but instead assuming that the pKa shifts to approximately 8 upon complexation, yields regions of colloidal instability roughly centered around [−]/[+] = 1 at each pH (see Table S2). This suggests that the colloidal stability of complexes of micelles with annealed charge distributions is controlled primarily by the overall degree of charge neutralization but that shifts in the corona pKa upon complexation affect the point at which charge neutralization occurs. While turbidimetric titrations provide insight into the colloidal stability during complex formation, the ability of the charge density to anneal may also affect the stability and rearrangement kinetics of the complexes on longer time scales. To this end, complexes were monitored by DLS over a period of 4 weeks, as shown in Figure 2. At pH 6.5, the complexes exhibited bimodal size distributions that remained stable for the entire 4-week period, regardless of which species (PSS or micelles) was present in excess. This result is consistent with the result at low pH (pH 4.5) and with previous work, in which

Figure 3. Turbidimetric titrations of (D/O)S(27-13) micelles with PSS-30 in acetate buffer at pH 4.5 and 10 mM ionic strength. Filled symbols indicate homogeneous mixtures, while open symbols indicate formation of a heterogeneous precipitate. 4635

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The Journal of Physical Chemistry B

were not stable indefinitelyaggregated over time,12,38 while those formed with the (D/O)S(27-13) micelles instead appeared to dissociate. The smaller size of the annealed complexes relative to the uncomplexed micelles suggests that the micelle coronas were still neutralized by complexed PSS even after annealing to single-micelle species. To further investigate whether this reduction in aggregate size corresponded to simple breakup of the neutral aggregates or complete dissociation of the bound PSS chains from the micelle coronas, we employed cryoTEM and ζ-potential measurements. As expected from DLS, cryoTEM images of the week-old complexes made with PSS in excess (Figure 5d) exhibited none of the multimicelle aggregates observed in the freshly made complexes with either PSS or micelles in excess (Figures 5b,c). The cryoTEM images of the week-old complexes did, however, reveal that these complexes appeared both slightly larger and much patchier than the uncomplexed micelles (Figure 5a), which is a characteristic signature of the formation of high-contrast polyelectrolyte complexes around the micelle core. Thus, the cryoTEM images suggest that the micelles remained complexed with the PSS after breakup of the multimicelle complexes. The ζ-potential measurements also confirmed that the micelles remained complexed with at least some of the PSS chains after breakup of the large multimicelle aggregates. As shown in Table 1, the complexes on day 7 had a ζ-potential of −26 ± 1 mV, only

Figure 4. Hydrodynamic radius distributions of complexes of (D/ O)S(27-13) micelles with PSS-30 in acetate buffer at pH 4.5 and 10 mM ionic strength. Samples were prepared at [−]/[+] values of 2.45 (excess PSS) and 0.41 (excess micelles).

complexes made with the micelles in excess remained relatively stable over more than 2 months, while those made with excess PSS rearranged to single-micelle complexes in less than a week. This behavior is surprising, since previous experiments on PDMAEMA-b-PS micelles yielded complexes thatif they

Figure 5. Cryogenic transmission electron microscope images of complexes of (a) (D/O)S(27-13) micelles and (b−d) their complexes with PSS-30, at (b) [sulfonate]/[amine] = 0.41 and (c, d) [sulfonate]/[amine] = 2.45 on (c) day 0 and (d) day 7 in acetate buffer at pH 4.5 and 10 mM ionic strength. Scale bar: 100 nm. 4636

DOI: 10.1021/acs.jpcb.7b01953 J. Phys. Chem. B 2017, 121, 4631−4641

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The Journal of Physical Chemistry B Table 1. ζ-Potentials (in mV) of Micelles, Complexes, and PSS in Acetate Buffer at pH 4.5 and 10 mM Ionic Strength complexes with PSS-30 polymer DS(30-8) (D/O)S(27-13) PSS alone

uncomplexed 28 ± 3 30 ± 2

[sulfonate]/ [amine] = 2.45

[sulfonate]/ [amine] = 0.41

−37 ± 1 −30 ± 1 (day 0) −26 ± 1 (day 7)

37 ± 2 28 ± 1

−10 ± 5

slightly less negative than that of the freshly formed complexes (−30 ± 1 mV) but significantly more negative than either the uncomplexed micelles, complexes formed with micelles in excess, or free PSS-30. Thus, while the ζ-potential measurements cannot eliminate the possibility that some of the PSS desorbed from the micelles during the rearrangement process,46 the data suggest that the rearrangement corresponded predominantly to breakup of the multimicelle aggregates rather than complete dissociation of the PSS−PDMAEMA complexes. Molecular Dynamics Simulations. Schematics of the brush system and snapshots of the MD simulations are shown in Figure 6. For the computational work, a brush was used rather than a micelle to decrease the simulation size. While this means that the simulations may miss subtle effects related to the interfacial curvature, we expect that the trends in the dynamics and thermodynamics of binding to the brush should be similar for micelles of the size considered in the experimental work (ca. 30 nm). While previous MD simulations on brush−polyelectrolyte complexes have focused on the structure of the complexes,47−49 our analysis focused on the kinetics and thermodynamics of the binding equilibrium. Figure 7 summarizes the polyion monomer exchange rate (the rate at which contacts between polyanions and polycation monomers are created and destroyed), free polyanion concentration, and electrostatic energy per particle for each of the polyanion:polycation ratios simulated using this model. The free polyanion concentration was similar in both the block and alternating brush models, suggesting that the charge sequence in the brush did not significantly affect the binding equilibrium. The electrostatic

Figure 7. Plots of (a) the rate of polyion contact turnover, in exchange events per Lennard-Jones time unit, τ, (b) free polyanion concentration, and (c) electrostatic energy per particle for both the block and alternating systems as a function of the number of polyanions in the system.

energy is lower for the block polycation brush system over the whole concentration range, including zero polyanion concentration. This indicates that both monovalent anions and polyanions bind more strongly to the block brush. However, the difference between the two energies changes relatively little over the concentration range, which indicates that the energy

Figure 6. (a) Illustration of the sequences of the block (left) and alternating (right) polymer brushes. (b) Snapshots of the block (left) and alternating (right) simulation systems. Small ions are omitted for clarity. Neutral monomers are shown in gray, cationic monomers in blue, and anionic monomers in red. 4637

DOI: 10.1021/acs.jpcb.7b01953 J. Phys. Chem. B 2017, 121, 4631−4641

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The Journal of Physical Chemistry B change associated with bringing a polyanion into the brush (the difference between binding a polyanion and an equivalent number of monovalent anions) is similar between the two brush types. Because the dominant entropic driving force for complexation (counterion release) is also similar for both brush types, the differences in electrostatic energies have little effect on the overall binding equilibrium.50−52 While the thermodynamic driving forces for complexation differ little between brush types, the individual energies are relevant for kinetics. As shown in Figure 7a, the kinetics of polyion monomer exchange were approximately an order of magnitude faster in the alternating brushes than in the block brushes, and exchange rates in both brushes were 1−2 orders of magnitude faster when the polyanion was in excess. This reflects the fact that breaking individual contacts is less energetically costly for the alternating brush isomer because the system with a cationic block and an anionic homopolymer tends to form structures in which each charged monomer can strongly interact with more than one monomer of the opposite charge. The observation that the rate of ion-pair exchange within the brush is enhanced for both brush types in the case of excess polyanions is nontrivial and is consistent with the experimental observation that micelles in which the hydrophilic block is a random copolymer equilibrate more rapidly in the presence of excess polyanions than in the case of excess polycation (i.e., excess micelles). While not explored in detail in the present work, this is likely analogous to the observation that exchange of surface-adsorbed polymers is faster in the presence of excess adsorbing chains that compete for binding sites.53−56

Table 2. Summary of pH- and Polymer-Dependent Rearrangement of Micelle−PSS Complexes rearrangement to single-micelle complexes

a

micelle

pH

[sulfonate]/[amine] = 0.41

DS(30-8) DS(30-8) DS(30-8) DS(30-8) (D/O)S(27-13)

4.5 6.5 7.5 8.5 4.5

no no yes N/Aa no

[sulfonate]/[amine] = 2.45 no no no no yes

Forms insoluble aggregates on mixing.

micelle complexes, while those formed with PSS in excess remained stable multimicelle aggregates. This behavior appears to result from the shift in pKa upon complexation with PSS. In the complexes formed with PSS in excess, the micelle corona becomes fully charged after complexation, leading to kinetically trapped complexes similar to those formed at low pH. In complexes formed with the micelles in excess, on the other hand, there remain many uncharged DMAEMA units within the corona. Fluctuations in the charge state due to the protonation−deprotonation equilibrium, and movement of protons between adjacent DMAEMA units, can then facilitate movement of the charged sites within the brush and help the complexes reach more favorable ion-pairing configurations. Charge annealing thus facilitates a rearrangement pathway that is not accessible to either the fully paired complexes formed with PSS in excess or the fully charged complexes formed at low pH. Importantly, while rearrangement from multimicelle to single-micelle complexes for samples prepared with excess cationic micelles has also been observed in high salt annealing experiments,12 the mechanism of this process appears to be somewhat different at high pH than at high ionic strength. At high ionic strength, rearrangement is facilitated by increased electrostatic screening, which allows interchain ion pairs to dissociate and find new partners more easily. At high pH, the rearrangement process is facilitated by the decreased charge density, which similarly lowers the energetic cost for ion pair dissociation, and also by the ability of the charge distribution to rearrange within the brush and form more favorable ion-pairing configurations. For (D/O)S(27-13) micelles, on the other hand, in which the charge distributions are fixed in place during the polymerization process, the opposite behavior is observed: complexes anneal toward single-micelle complexes only if the polyanion is in excess but remain stable as multimicelle aggregates if the micelles are in excess. This behavior is counter to that observed in either high salt or high pH annealing of complexes of PDMAEMA-b-PS micelles.12 The stability of the complexes formed with micelles in excess suggests that although diluting the charge density may weaken the overall binding between the polyanion and polycation chains, the barrier to rearrangement is higher when dissociation of an anion from the cationic brush leaves behind a cationic unit that must stay charged (as in (D/O)S(27-13) at low pH) than when it leaves behind a cationic unit that may then deprotonate to give an uncharged site (as in DS(30-8) at elevated pH). This difference no longer matters when the polyanion is in excess because all DMAEMA units in both the DS(30-8) and (D/O)S (27-13) micelles remain charged throughout the polyion exchange processes. Unlike the DS(30-8) system, however, the charge distribution in the (D/O)S(27-13) micelles remains

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DISCUSSION Comparison of the rearrangement kinetics for complexes of (D/O)S(27-13) and DS(30-8) with the same polyanion (here, PSS-30), in conjunction with the MD simulations on complexation with blocky and alternating polymer brushes, provides important insight into how charge distribution affects both the complexation process and subsequent annealing toward thermodynamic equilibrium in polyelectrolyte complexes. The complexes exhibited similar titration behavior in both systems, becoming colloidally unstable near the chargeneutral point at [−]/[+] = 1 and exhibiting bimodal size distributions consistent with the formation of multimicelle aggregates. This suggests that the initial complexes of both micelle types form similar nonequilibrium structures. Both systems also exhibit rapid rearrangement, in contrast to the DMAEMA-only micelles at low pH and ionic strength. Because complex rearrangement, and particularly deaggregation, necessarily requires relaxation and mobility of the adsorbed polyanion chains, this observation suggests that reducing the charge density promotes chain motion by reducing the ion pair binding strength and the energetic barrier for rearrangement of chain−chain contacts. This conclusion is further supported by the electrostatic energy difference between the block and alternating cases in the MD simulations. However, as summarized in Table 2, the type of rearrangement observed is different for the DS(30-8) and (D/O)S(27-13) micelles, signaling that there are important differences in either the mechanisms or thermodynamics underlying rearrangement processes in complexes with quenched and annealed charge distributions. For DS(30-8) micelles above the pKa of the PDMAEMA brush, in which the charge distributions can anneal, complexes formed with micelles in excess rearranged to form single4638

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The Journal of Physical Chemistry B diluted even at high polyanion:polycation ratios. In combination with the excess of polyanion chains available to move in and out of the brush (and within the brush), this dramatically increases the ability of complexes of (D/O)S(27-13) micelles to rearrange. Finally, while the present analysis assumes that the bulky PEG side chains are spectators that do not affect the rearrangement process beyond reducing the average charge per monomer, it may be useful to investigate in future work whether steric hindrance of complex formation plays a role in accelerating rearrangement. A number of studies have investigated the role of charge density in the composition, structure, and overall stability of polyelectrolyte complexes. However, far less attention has been paid to its role in the kinetic and dynamic properties of these materials and to the extent to which the static or dynamic nature of the charge distribution changes these properties. This work suggests that further investigation is needed on this front. In particular, expanding rheological studies of the pH and salt dependence of complex coacervates to include materials with fixed charge distributions will provide important information on how charge density affects the dynamics of polyion contacts. Single-molecule force measurements and atomistic MD simulations may also provide complementary information about how charge density and charge annealing affect binding strengths in these materials.26−29,57 This information will provide important new avenues for understanding and controlling dynamic processes in polyelectrolyte complex materials.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Jennifer E. Laaser: 0000-0002-0551-9659 Theresa M. Reineke: 0000-0001-7020-3450 Timothy P. Lodge: 0000-0001-5916-8834 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank Charles Sing for helpful discussions. This work was funded by the National Science Foundation through the University of Minnesota Materials Science Research and Engineering Center (DMR-1420013). 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. was supported in part by a fellowship through the L’Oréal For Women in Science Postdoctoral Fellowship program. Computational resources were provided in part by the Minnesota Supercomputing Institute.

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REFERENCES

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CONCLUSIONS Rearrangement in polyelectrolyte−micelle complexes depends strongly on the charge distribution in the micelle coronas. Importantly, while reducing the charge density generally reduces the barrier to rearrangement and speeds rearrangement kinetics, the ability of the charge distribution to anneal in response to complexation also plays a critical role in determining the rearrangement pathways available to the complexes. When the charge distribution can anneal, as in the DS(30-8) micelles at elevated pH, complexes formed with micelles in excess can rearrange by migration of ion pairs and charged sites within the brush. Those formed with the polyanion in excess, on the other hand, are kinetically trapped as the charge density shifts to favor fully charged, fully ionpaired configurations. However, when the charge distribution cannot anneal, as in the (D/O)S(27-13) micelles, the opposite behavior is observed. Complexes formed with the polyanion in excess rearrange, indicating that they retain the kinetic advantages of the reduced charge density, making otherwise inaccessible rearrangement pathways feasible. While this work was conducted for polyelectrolyte−micelle complexes, many of the conclusions related to the role of charge annealing should be applicable to other types of polyelectrolyte complexes as well and suggest that controlling charge density should be a viable strategy for controlling equilibration kinetics and dynamic processes in a wide range of polyelectrolyte complex materials.

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Synthetic and characterization data for polymers, turbidimetric titration, and dynamic light scattering results (PDF)

ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcb.7b01953. 4639

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