Tunable Coacervation of Well-Defined Homologous Polyanions and

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Research Article Cite This: ACS Cent. Sci. XXXX, XXX, XXX−XXX

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Tunable Coacervation of Well-Defined Homologous Polyanions and Polycations by Local Polarity Junzhe Lou,†,∥ Sean Friedowitz,†,∥ Jian Qin,*,‡ and Yan Xia*,§ †

Department of Materials Science and Engineering, Stanford University, Stanford, California 94305, United States Department of Chemical Engineering, Stanford University, Stanford, California 94305, United States § Department of Chemistry, Stanford University, Stanford, California 94305, United States ‡

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ABSTRACT: The ionic complexation of polyelectrolytes is an important mechanism underlying many important biological processes and technical applications. The main driving force for complexation is electrostatic, which is known to be affected by the local polarity near charge centers, but the impact of which on the complexation of polyelectrolytes remains poorly explored. We developed a homologous series of well-defined polyelectrolytes with identical backbone structures, controlled molecular weights, and tunable local polarity to modulate the solvation environment near charged groups. A multitude of systematic, accurate phase diagrams were obtained by spectroscopic measurements of polymer concentrations via fluorescent labeling of polycations. These phase diagrams unambiguously revealed that the liquidlike coacervation is more stable against salt addition at reduced local polarity over a wide range of molecular weights. These trends were quantitatively captured by a theory of complexation that incorporates the effects of dispersion interactions, charge connectivity, and reversible ion-binding, providing the microscopic design rules for tuning molecular parameters and local polarity. separate into a distinct polymer-rich “coacervate” phase and a dilute supernatant that is nearly devoid of all polyelectrolytes. While the earliest report on polyelectrolyte complexation can be traced back to 1927,1 many questions still remain regarding the detailed thermodynamic factors at play in the process. The fundamental complication of polyelectrolyte complexation results from the interplay of physical interactions spanning a wide range of length scales and dependent on various factors, including the long-range Coulombic forces, mixing entropies of constituent species, and local steric and dielectric effects.13 As such, the formation of PECs depends on many parameters, such as the molecular weight14 and chemical structure15 of polymers, polymer backbone chirality,16 structure and sequence of charges,17 and salt valence.18 Theoretical descriptions of the polyelectrolyte complexation have evolved significantly in the past. The classical theory of Voorn and Overbeek (VO) portrayed this process as resulting

1. INTRODUCTION Polyelectrolyte complex coacervates (PECs) are liquidlike droplets formed from solutions of oppositely charged polyelectrolytes.1 They are concentrated in polymers, stabilized by interfacial tension with the supernatant, and may coalesce over a long period of time, evolving into a macroscopic continuum. Owing to their unique liquid-phase stability and tunable rheological responses, PECs have attracted growing interest in a variety of applications, including the encapsulation of biomolecules and drug delivery depots,2−4 tissue culture scaffolds,5 bioreactors,6 and surface adhesives.7 More recently, the formation of PECs has been recognized as an effective mechanism leading to the formation of membraneless compartments in biological systems.8−11 PECs are found to participate in the formation of liquid organelles in eukaryotic cells,8,9 protect DNA structures and regulate transcription,10 promote cyclic GMP-AMP production to innate immune signaling,11 and provide surface adhesion for marine organisms under water.12 Underlying the coacervation process is a thermodynamic instability that drives polyelectrolytes to © XXXX American Chemical Society

Received: December 24, 2018

A

DOI: 10.1021/acscentsci.8b00964 ACS Cent. Sci. XXXX, XXX, XXX−XXX

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complexation beyond what is determined solely by hydrophobicity. Therefore, to probe how the local environment surrounding polyelectrolyte charges affects the stability of complex, it would be ideal to only modulate the hydrophobicity of polyelectrolyte chains without altering the structures of charged groups or polymer backbones, polymer molecular weight, or chain stiffness. Synthetic polyelectrolytes prepared by controlled polymerization have enabled precise control of molecular weight and charge density. Hawker and co-workers reported the synthesis of ABA triblock copolyelectrolytes with poly(ethylene glycol) backbones using ring-opening polymerization. The charge groups were tethered to the end blocks of the same parent polymers, ensuring identical polymer length and number of ionic groups on each polymer.49 Mixing two copolymers with oppositely charged end blocks resulted in hydrogel formation at near charge stoichiometry due to the formation of microphase-separated, ordered structures.49−51 Inspired by their work, we synthesized a series of polyelectrolyte homopolymers with polyacrylamide backbones via reversible addition−fragmentation chain transfer (RAFT) polymerization, with identical charge density and controlled molecular weights. In particular, the charged groups were linked by alkyl sulfide side-chains, and the facile oxidation of alkyl sulfide to more polar sulfoxide provided a unique means to modulate the local polarity in proximity to the charged groups with minimum changes in polymer structure. This system enabled independent tuning of the local hydrophobicity surrounding polyelectrolyte charges and allowed us to unambiguously demonstrate the profound effect of local charge environment on the phase separation behavior of PECs. We further developed a robust fluorescent labeling protocol to allow accurate quantification of polymer concentrations in the coacervate and solution phases. This work represents the first study of polyelectrolyte phase behavior using well-controlled polymers with three advantageous features: identical backbones for the polyanions and polycations, tunable local polarity in proximity of charged groups with minimal structural perturbation, and an accurate spectroscopic method for determining the composition of the coacervate and solution phases. These developments enabled us to quantitatively analyze experimentally determined phase diagrams in the context of a thermodynamic model recently developed by some of us that relies on a description of reversible ion-binding.33,52 The experimental and predicted phase diagrams using our theory showed excellent agreement. The results demonstrate that a single solubility parameter measuring the strength of solvent−polyelectrolyte interactions is sufficient to capture variations in complexation stability with changes in molecular weight and local polarity of the polyelectrolytes.

from the competition of the mixing entropy, which favors a homogeneous solution, and Debye−Hü ckel correlations, which favor complexation.19 However, it is well-established that this simple model neglects various essential physics for the complexation process.20 More sophisticated modifications of the VO model have been proposed, incorporating effects such as dispersion interactions,14,21,22 dipolar interactions,23−25 liquid-state correlations,26,27 chain connectivity and adaptive chain structures,28,29 and reversible charge binding equilibrium.30−33 Coarse-grained computational approaches have provided refined views regarding the complexation process, allowing effects such as interspecies correlations,34−36 salt partitioning between phases,35,37 and the formation of microphase structures38 to be probed in detail. A common theme among these emerging approaches has been a focus on the effects of short-range charge interactions in driving complexation behavior, beyond that of the long-range Coulomb forces included in the original VO model. The wealth of microscopic details in PECs has offered the necessary support and guidance for the theoretical developments outlined above. Comparisons between experimental and theoretical or simulation results have been reported;14,39 however, quantitative investigations are rare and often lack good agreement between the two, largely owing to the difficulty of preparing carefully controlled samples and calibrated phase diagrams over a wide range of parameter space, including variation in salinity, molecular weight, and mixing ratios. To start filling this gap, we aimed to develop a simple model system to elucidate the effects of the local chemical environment surrounding the bound charges on the polyelectrolyte chains, which is not readily probed theoretically but can be conveniently modified through synthetic means. The local charge environment characterizes how ions are solvated by the surrounding medium or, equivalently, how the medium is polarized by the ions. The strength of electrostatic interactions has been broadly conceived as an important factor for regulating protein−protein binding strength and modulating the conformational properties of proteins.40−43 For example, electrostatic interactions in hydrophobic environments are known to be stronger than those exposed to hydrophilic surfaces.40,44 Recently, it was found both theoretically and experimentally that ion-pairing is enhanced in aqueous media when approaching a hydrophobic surface.45−47 For example, ionic head groups were tethered to a hydrophobic substrate via a flexible chain within a selfassembled monolayer of alkyl chains with different chain lengths to modulate the distance of the charges to the surface.45 The electrostatic interactions closer to the hydrophobic surface were found to be stronger and more resistant to variation in external conditions (e.g., pH and electric field). In this work, we investigate and unambiguously reveal the impact of the local environment on the formation of PECs. Recent experiments have shown, by varying the structure of charged groups, that the strength of electrostatic interactions and the stability of PECs correlated with the degree of hydrophobicity: more hydrophobic charged moieties formed more stable complexes with higher resistance to salt addition.15,48 However, considering the complexity of PECs, structural changes of charged moieties and polymer backbones could potentially result in different charge distributions and pKa values, as well as introduce additional effects such as π−π or cation−π interactions, which may all affect the degree of

2. RESULTS AND DISCUSSION 2.A. Polymer Synthesis and Polarity Control. We sought a general strategy to synthesize a series of anionic and cationic polyelectrolytes from an identical polymer backbone with controlled molecular weight, charge density, and variable local polarity. We first synthesized a series of poly(Nacryloxysuccinimide)s with controlled degrees of polymerization N = 50, 100, and 180 and low dispersity (Đ) via RAFT polymerization (Figure S1). The trithiocarbonate chain end was then removed via radical induced reduction using silane, followed by quantitative aminolysis of all the succinimide B

DOI: 10.1021/acscentsci.8b00964 ACS Cent. Sci. XXXX, XXX, XXX−XXX

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Figure 1. (a) Synthesis and chemical structures of the anionic and cationic polyelectrolytes with identical polyacrylamide backbones. (b) Chemical structure of RB-labeled cationic polyelectrolyte. (c) Oxidation study of a model sulfide with the product distribution after treating with different molar equivalents of H2O2.

and 14% of unreacted sulfide. Further increasing H2O2 to 2.0 equiv resulted in 43% of sulfoxide and 57% of sulfone. We also confirmed that both ammonium and sulfate groups are stable in aqueous solution under the H2O2 oxidation conditions (Figure S5). Therefore, oxidation of the side-chain sulfide groups provides a convenient and controlled means to continuously tune the polarity without affecting the charged groups. Our design allowed us to systematically vary the molecular weight and local polarity of polyelectrolytes, two important parameters for complexation, independently and continuously. To investigate their effects on PECs, three sets of polyelectrolytes with degree of polymerization N = 50, 100, and 180 were each treated with 0, 0.1, and 0.5 equiv of H2O2 to vary the fraction of formed sulfoxide. In addition, to accurately quantify the polymer concentration in different phases upon mixing oppositely charged polyelectrolytes, a widely used water-soluble fluorescent dye, Rhodamine B (RB), was sparsely conjugated to the cationic polymers via aminolysis (Figure 1b). The amount of dye labeled on polycations is approximately 1 RB per 10 polymer chains, on average, based on the integrations from 1H NMR spectroscopy (Figure S6). Considering the positively charged nature of RB and sparse conjugation on the polymers, RB labeling has negligible effect on charge density of the polycations. We have also confirmed that the fluorescence of RB remained unchanged upon H2O2 treatment, which assured the quantitative analysis of polymer concentrations after oxidation with H2O2. 2.B. Binodal Phase Diagram Characterization. Solutions of anionic and cationic polyelectrolytes of the same chain length and polarity were mixed at 1:1 molar ratios with varying NaCl concentrations ranging from 0 to 1.5 M. Complexation between oppositely charged polyelectrolytes in aqueous solution resulted in rapid phase separation into a polymer-rich coacervate phase and a polymer-poor supernatant phase (Figure 2a). The pink color from conjugated RB allowed

activated ester groups on the polymers to generate poly(allyl acrylamide). The pendent alkenes allowed facile functionalization via thiol−ene reactions to introduce charged moieties, sulfate and ammonium (Figure 1). Either 2-mercaptoethylammonium chloride or sodium 3-mercapto-1-propanesulfonate was attached to poly(allyl acrylamide) via UV light-mediated (365 nm) thiol−ene radical reactions in aqueous solutions. Nuclear magnetic resonance (NMR) spectroscopy showed complete and clean conversions for both aminolysis and thiol− ene reactions (Figures S2 and S3). Thus, a pair of well-defined cationic and anionic polyelectrolytes were obtained with hydrophilic polyacrylamide backbones and a high density of charges. The synthesis of each pair of polyelectrolytes from the same parent polymer resulted in chains with identical lengths and numbers of ionic groups, which eliminated potential uncertainties of charge imbalance and chain length mismatch during PEC formation.49 We then took advantage of the sulfide moiety on each polymer side-chain to modulate chain polarity. Sulfide is known to be easily oxidized to sulfoxide (dipole moment μ = 3.96 D for dimethyl sulfoxide) and sulfone (μ = 4.49 D for dimethyl sulfone), which are more polar than sulfide (μ = 1.5 D for dimethyl sulfide) due to their strong dipoles.53 Therefore, controlled degrees of sulfide oxidation would provide a convenient means to modulate the local polarity around the charges with minimal structural perturbation. To study the extent of sulfide oxidation, 3,3′-thiodipropionic acid was chosen as a model compound to react with H2O2 (Figure 1), which is an ideal oxidant since water is the only generated byproduct without creating any new chemical species in the PEC system. When 0.5 equiv or less of H2O2 was used, sulfide moieties were cleanly oxidized to sulfoxide in proportion to the stoichiometry of H2O2 used, as monitored by the α-proton signals using 1H NMR spectroscopy (Figure S4). When higher equivalents of H2O2 were applied, a mixture of sulfoxide and sulfone groups were generated. Using 1.0 equiv of H2O2, the reaction produced 12% fully oxidized sulfone, 74% sulfoxide, C

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Figure 2. (a) Photograph of phase separation upon mixing of oppositely charged polyelectrolytes at different concentrations of added NaCl (N = 50, 0 equiv H2O2). The pink color resulting from fluorescently labeled polycations showed cleared differences in polymer concentration between the two phases. Experimental phase diagrams for the (b) N = 180, (c) N = 100, and (d) N = 50 polyelectrolytes at different extents of side-chain oxidation. The y-axis represents the total concentration of salt ions, and the x-axis represents the determined total polymer concentration in each phase. The ion concentration in the two phases was assumed to be equal. Error bars in measured polymer concentration are so small that they roughly fall within the size of each data point.

Comparison of the binodal phase diagrams for polymers with different chain lengths showed that longer polymer backbones led to a greater coacervate stability under equal amounts of added salt. We quantified this stability by comparing the upper maximum ion concentration (c*S ) on each phase diagram, which was recorded as the bulk ion concentration of the highest point on each binodal curve assuming equal salt partitioning between the two phases. For example, c*S for the shortest (N = 50) and longest (N = 180) polymers, with no H2O2 oxidation, was determined to be 2.2 and 2.9 M, respectively. In addition, longer polymers exhibited a wider two-phase region, characterized by a larger difference in polymer concentration between the two phases. For example, the polymer concentration in the coacervate phase without added salt or sulfide oxidation increased from 1.8 to 2.2 M with an increase in chain length from N = 50 to N = 180. These results are consistent with the previous reports from the Cohen Stuart and Tirrell groups,14,54 and can be rationalized by the decreased translational entropy of the polymer chains with increasing chain length, which results in a lesser entropic penalty for chain sequestration in the denser coacervate phase. Side-chain polarity also significantly affected the phase diagrams. The maximum ion concentration before coacervate redissolution was found to decrease significantly as the linker polarity was increased (Figure 3). For polyelectrolytes with N = 50, the maximum ion concentration was reduced nearly by one-half when oppositely charged polyelectrolytes were both treated with 0.5 equiv H2O2 before mixing. With increasing local polarity, the polymer concentration in the coacervate phase also decreased slightly with a simultaneous increase in the volume of coacervate (Figure S10). For example, the coacervate concentration for the N = 50 polyelectrolytes without added salt decreased from 1.8 to 1.6 M as 0.5 equiv H2O2 was added to partially oxidize sulfide groups. Such differences appeared to become more significant with increasing salt concentration. We attributed the swelling and

clear visualization of the much higher polymer concentrations in the bottom coacervate layer than the supernatant layer. To quantify this phase separation, the extinction coefficient of the RB-labeled polycations was measured at 566 nm absorption and used to determine the polyelectrolyte concentrations in both the coacervate and solution phases, under the assumption that NaCl concentrations were equal in both phases. Investigating the partitioning of salts in order to address a point of discussion in the literature27,32,35,37 demands the direct measurement of salt concentrations. The extinction coefficient of RB is pH sensitive (Figure S7) with maximum absorption at pH 4.2, and therefore all the measurements were performed by diluting a measured small aliquot of the coacervate or supernatant to a buffer solution at pH 4.2. Further, high concentrations of NaCl or varying the mixing ratio of the polycations and polyanions from 1:1 to 1:2 had negligible effect on the extinction coefficient of the RB-labeled polycations (Figures S8 and S9). Thus, with this method we can accurately quantify the concentration of polycations in phase-separated PECs under different salt concentrations, stoichiometry of polyanions, and degrees of sulfide oxidation. Salt−polymer phase diagrams were plotted for each polyelectrolyte chain length and extent of sulfide oxidation (Figure 2b−d). In these diagrams, the y-axis represents the total concentration of salt ions in the system ([Na+] + [Cl−]) including the counterions of the polyelectrolytes, and the x-axis represents the total polymer concentration. Added salt played an important role of weakening the PECs due to ionic screening, and eventually resulted in dissolution of the complexes at high enough concentrations. Increasing the salt concentration resulted in the gradual decrease of polymer concentration in the coacervate phase, and simultaneous increase of polymer concentration in the solution phase. Past a maximum ion concentration, a homogeneous solution was reobtained. Trends in the effect of ion concentration were clearly observed as a function of polyelectrolyte length and degrees of sulfide oxidation (Figure 2b−d). D

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bound charge pairs;52 and fχ is the Flory−Huggins interaction accounting for the dispersion interactions between polymer chains and solvent. Since the mixing free energy f T is standard, and the electrostatic correlation term fel has been extensively treated,28 the remaining discussion will provide only a general picture of the model, while the algebraic details are given elsewhere.33,52 The free energy depends on the volume fractions and monomer volumes of each component, the statistical segment lengths of the chains, the medium dielectric permittivity (ϵr = 80 for water at room temperature), specific binding energies for each type of reversible ion-binding, the Flory−Huggins χparameter between the polyions and solvent, and a series of bound ion fractions for each type of reversible binding. These bound ion fractions include αA+ for cation-binding along the polyanions, αC− for anion-binding along the polycations, and βA and βC for ion-pair formation between the polyanions and polycations, respectively. However, as ion-pairing only occurs between oppositely charged chains, we can relate the two ionpairing fractions through a stoichiometry constraint, and write βA as a function of βC.33 Then, for a given set of compositions and binding free energies, the degrees of ion association are determined by minimizing the solution free energy (eq 1) with respect to αA+, αC−, and βC, subject to the constraint of stoichiometric ion-pairing. The results can be expressed in terms of a set of the laws of mass action with effective association constants of the form

Figure 3. Comparison of the maximum total concentration of salt ions recorded on the binodal diagram for each combination of chain length and oxidation level. A consistent decrease in cS* was observed with decreasing N and increasing local polarity.

volume expansion of the coacervate to the increase in the local polarity around charged groups within the coacervate phase upon oxidation of the hydrophobic sulfide linker to the more polar sulfoxide. The local polarity is expected to affect electrostatic interactions between the polyelectrolyte charges owing to the change of solvation shell around charges and dielectric constant in the vicinity of charges. Further increasing the amount of added H2O2 had only a weak effect on c S* . For example, for the N = 180 polyelectrolytes, when added H2O2 increased from 0.5 to 2.0 equiv, c*S only decreased from 1.7 to 1.5 M. We attributed this observation to a similar solvent−polyelectrolyte interaction parameter in these two systems, as quantified by the Flory− Huggins χ-parameter. For instance, initial oxidation of the sulfide groups to sulfoxide (less than 0.5 equiv H2O2) yielded a dramatic decrease in the χ-parameter (see next section for accurate value). However, after more than 50% of sulfides were converted to sulfoxides, further oxidation would have a minor effect on modifying the solvation environment, and the χparameter may plateau, although the effect of higher oxidation levels for other types of polymers remains to be tested. Therefore, the phase diagrams for polymers treated with 0.5 equiv or 2.0 equiv H2O2 were similar (Figure 2b). This effect was quantified in our theoretical analysis presented next, which allowed the χ-parameter to be determined for each level of side-chain oxidation. 2.C. Theoretical Analysis. The trends in the above experimental phase diagrams can be quantitatively captured by using a simple free energy model for polyelectrolyte solutions. The model is built upon the previous work33,52 and explicitly treats reversible ion-binding,33,52 including anion localization near polycations, cation localization near polyanions, and the formation of interchain “ion-pairs” or cross-links between polycations and polyanions. At the heart of the model is an expression for the solution free energy density that contains five additive contributions: f = fT + fel + fC + fad + f χ

K i ∝ e−(ΔGi + μi )/ kBT

(2)

where the index i represents each of the three types of ion association (Figure 4), ΔGi is the specific binding energy for

Figure 4. Schematic of the three types of reversible ion-binding considered in our model. The effective association constants are KA+ for cation-binding along the polyanions, KC− for anion-binding along the polycations, and Kβ for interchain cross-linking between the polyanions and polycations.

charge pair formation appearing in fad, and μi is an excess chemical potential of charged species stemming from the longrange electrostatic interactions in the system. In this work, we extend the earlier ion-binding formalism33 by treating the electrostatic free energy, fel, with a modified Gaussian fluctuation theory,28 which explicitly includes the effects of chain connectivity and self-interactions between bound charges on the chains. By including these electrostatic self-interactions in the model, the resulting excess chemical potential appearing in the laws of mass action represents a favorable driving force for binding of oppositely charged species, as reported previously.52 When calculating phase diagrams with this model, the above laws of mass action are solved numerically to self-consistently determine the ionbinding fractions as a function of composition. In the case of symmetric polymer and salt volume fractions, polymer charge density, and structures of the polyions, the counterion-binding

(1)

The term f T is the translational entropy for all species including the solvent, small ions, and polyions; fel is the electrostatic correlation free energy among ionic species;28 f C is a combinatorial factor accounting for the number of ways to form reversible binding pairs, including those between cations and polyanions, anions and polycations, and polycations and polyanions;33 fad is the adsorption free energy for forming E

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and hydrophilicity. Moreover, the value of χPW appears to saturate with levels of oxidation, which falls in line with the experimentally observed saturation of the maximum ion concentration (Figure 2a). We stress that a single χPWparameter has captured the results for polymers with different molecular weights, which is possible only because of the homologous polyions used. The comparisons between theoretical predictions and experimental phase diagrams are shown in Figure 5, for the three chain lengths examined. The maximum ion concentration and the width of two-phase window for all four levels of side-chain oxidation are captured quantitatively for the case of N = 180 (Figure 5a). This excellent agreement suggests that the effect of local polarity in solution of homologous polyions can be conveniently represented by a single χ-parameter. The agreement for the cases of N = 100 and 50 at all levels of oxidation (Figure 5b,c) is even more remarkable, given that the parameters used in these theoretical predictions were obtained from independent fitting for the system with N = 180. The theory, despite its simplicity, has captured the effects of molecular weight, monovalent salt addition, and local polarity. We stress that this level of agreement is obtained only if charge connectivity, dispersion interactions, and reversible ion-binding are all considered. The original VO model19 failed to capture, in particular, the width of two-phase window. More quantitative analyses further show that variations in the maximum ion concentration can be summarized by a scaling form, cS* ∼ Nγ, with an experimental exponent γ ≈ 0.2 and a theoretical value γ ≈ 0.12, regardless of the level of oxidation. Thorough analysis of this behavior and the performance of alternative theoretical models will be presented in due course.

and ion-pairing fractions become equivalent, i.e., αA+ = αC− and βA = βC. Two types of model parameters need to be fixed to apply the above theory to rationalize the experimental phase diagrams. The first type relates to the adsorption free energy term fad. Three binding energies appear in this free energy contribution: ΔGA+ for cation−polyanion-pairing, ΔGC− for anion−polycation-pairing, and ΔGβ for the formation of interchain crosslinks. These terms are introduced to capture any specific interactions between the oppositely charged pairs,31,33,55 which dictate the degree of ion association through eq 2. In this work, these parameters are prescribed constant values that yield the best agreement to the experimental results (see below) and do not vary with molecular weight, hydrophobicity, or composition.33 The second type relates to the dispersion free energy capturing the interactions between solvents and both polycation and polyanion: f χ = χPW ϕPϕW

(3)

which has been previously combined with the standard VO model14,22 and used to analyze experimental results.14 Here, ϕP is the total polymer volume fraction, ϕW the solvent volume fraction, and χPW the Flory−Huggins parameter between the polymers and solvent. Because the backbone and side-chain groups for the polycations and polyanions are identical, a single χPW is used. Larger values of χPW correspond to a greater interaction penalty between solvent and polymer, and hence a greater tendency for phase separation. It is worth noting that varying local polarity potentially changes the strength of dielectric screening, which is not accounted for by the χPWparameter to minimize the number of fitting parameters used. The excellent agreement between the model and experimental results (see below) suggests the simplification has a negligible effect. The binding energies in the theory are varied to best match the experimental phase diagrams. Since the values of these parameters have been measured to be on the order of kBT,15,56 for simplicity, we set ΔGA+ = ΔGC− = −3.5kBT and ΔGβ = −4.0kBT, irrespective of molecular weight and hydrophilicity. The Flory−Huggins parameter χPW is then varied to capture the trends with variations in side-chain polarity. For each level of oxidation, we fit χPW to match the upper maximum ion concentration for the N = 180 samples, and use these values as inputs for the cases with N = 100 and N = 50. We note that the value of χPW depends on the value of ion-binding strength, which has been set to match the values calibrated in experiments.33 The fitted values of χPW are tabulated in Table 1. It is evident that higher oxidation levels yield lower values of χPW, consistent with the expected increments in side-group polarity

3. CONCLUSION In summary, we have developed a series of well-defined polyelectrolytes with identical structures except for the charged groups, controlled molecular weights, and tunable local polarity to closely examine the phase behavior of PECs. Oppositely charged polyelectrolytes were synthesized from a common polymer precursor made by RAFT polymerization and conjugated with charged moieties via thiol−ene chemistry to achieve identical molecular weight and charge density. The sulfide linker for charged groups on the resulting polymers can be easily and cleanly oxidized to more polar sulfoxide and sulfone groups, providing a convenient platform to modulate local polarity with minimum change of polymer structure. We accurately determined the polymer concentrations in coacervate and supernatant phases and obtained binodal phase diagrams of these polyelectrolytes, which were found to be strongly dependent on polymer molecular weight and local polarity. Increasing molecular weight coincided with a higher coacervate stability against the addition of salt. Similarly, increasing local polarity at higher extents of sulfide oxidation led to smaller two-phase regions and lower maximum salt ion concentrations. Trends in phase separation behavior were analyzed theoretically with a novel thermodynamic model relying on a description of reversible charge association. Side-chain oxidation and local polarity were mapped to a single χparameter between the solvent and polyelectrolyte species, χPW. Using χPW as a fitting parameter allowed us to capture reductions in both the maximum ion concentration and the width of the two-phase region with increasing extents of oxidation. Moreover, the variation of maximum ion concen-

Table 1. Fitted Solvent−Polyelectrolyte χ-Parameters to the N = 180 Experimental Phase Diagrams, Assuming a Reference Volume of the Aqueous Solvent v0 = 3.0 × 10−29 m3 H2O2 (equiv)

χPW

0.0 0.1 0.5 2.0

0.556 0.531 0.472 0.445 F

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Figure 5. Experimental phase diagrams (◆) and theoretical predictions () using the charge binding model for the (a) N = 180, (b) N = 100, and (c) N = 50 samples with varying extents of side-chain oxidation. The solvent−polyelectrolyte Flory parameter, χPW, is used to fit the theoretical model to the maximum salt fraction for the N = 180 sample for each degree of side-chain oxidation. The volume of the repeat units is calculated from the density and molecular weight of the polyions, and its cube root is chosen as the statistical segment length.

Schlenk tube. After 3 cycles of freeze−pump−thaw, the solution was heated at 80 °C for 4 h. The mixture was then cooled to room temperature and precipitated into diethyl ether twice. End group removal was confirmed by the disappearance of the absorption peak at 310 nm from trithiocarbonate. Poly(N-acryloxysuccinimide) was then modified via aminolysis to install terminal alkene functional groups on polymer side-chains. Poly(N-acryloxysuccinimide) (4 g) was dissolved in anhydrous DMF (40 mL) under nitrogen. After adding allyl amine (6.75 g, 5 equiv per monomer unit), the solution was stirred at room temperature overnight, during which time precipitant was formed due to the generated N-hydroxysuccinimide. The precipitant was filtered, and the solution was added to diethyl ether to precipitate the poly(N-allyl acrylamide) twice. Polyelectrolytes with sulfate or ammonium groups were prepared via thiol−ene reactions according to literature procedure with minor modifications.49 In a typical thiol−ene reaction, poly(N-allyl acrylamide) (1.2 g), 2mercaptoethylammonium chloride or sodium 3-mercapto-1propanesulfonate (8 equiv per alkene), and a radical photoinitiator 2,2-dimethoxy-2-phenylacetophenone (139 mg, 0.05 equiv per alkene) were dissolved in a mixture of water/ methanol (2:1, 40 mL) in a 100 mL round-bottom flask (quartz). The solution was deoxygenated by bubbling nitrogen for 30 min and irradiated with 365 nm light in a photochemical reactor (Luzchem) for 3 h. The resulting solutions were then dialyzed against deionized (DI) water for 3 days and lyophilized to obtain the desired polyelectrolytes as white powders. 4.B. Fluorescent Labeling of Polyelectrolytes. Rhodamine B (RB) was conjugated to positively charged polyelectrolytes at 3 different molecular weights. RB was first reacted with N-hydroxysuccinimide to form the activated ester (RB-NHS) via carbodiimide coupling (details in the SI). The polycation (2.7 g) was dissolved in a mixture of water/ dimethyl sulfoxide (1:1, 30 mL) in a 100 mL round-bottom flask. Triethylamine (TEA, 2 mL, 1.2 equiv to ammonium groups on the polyelectrolyte) was added to neutralize the side-chain ammonium. After removing water and extra TEA under reduced pressure, RB-NHS (30 mg, 0.004 equiv per amine) was added to the polymer solution. The mixture was stirred at room temperature overnight, neutralized using 1 M HCl, dialyzed against DI water for 3 days, and lyophilized to give the labeled polycation as a pink powder. The extinction coefficient of labeled polycations was measured by the absorption at 566 nm via UV−vis

tration with chain length is captured, leading to excellent agreements between experiments and model predictions over a wide range of parameters (Figure 5). Our experimental and theoretical investigations quantitatively revealed the role of two fundamental physical parameters in dictating stability windows for the formation of ionic complexes. Considering the critical roles PECs play in nature and important technological applications, insights from this work will guide the rationalization and active manipulation of the phase separation behavior in a myriad of complex biological and physical settings, such as targeting specific protein sequences that may be prone to ionic complexation or designing polyelectrolytes with tunable sensitivity to salt. While our work is focused solely on chain length and local polarity effects, there exist a wealth of other fundamental parameters, such as chain stiffness, charge patterning, and chemospecific interactions, that could be similarly analyzed based on the experimental and theoretical platforms described herein.

4. EXPERIMENTAL METHODS 4.A. Polyelectrolyte Synthesis. The synthesis of polymer precursors was achieved via RAFT polymerization. To prepare poly(N-acryloxysuccinimide) with a target degree of polymerization N = 50, N-acryloxysuccinimide (8 g, 47.3 mmol), 2(dodecylthiocarbonothioylthio)-2-methylpropionic acid (344 mg, 0.94 mmol), 2,2-azobis(2-methylpropionitrile) (AIBN, 31.2 mg, 0.19 mmol), and dimethylformamide (DMF, 16 mL) were added to a 100 mL Schlenk tube. After 3 cycles of freeze−pump−thaw, the polymerization was carried out at 70 °C for 2 h. The mixture was then cooled to room temperature and precipitated into diethyl ether twice. The polymer was isolated after filtration and drying in vacuo. The degree of polymerization was determined by comparing the integrations of 1H NMR signals of the end group and repeat units. The molecular weight and molecular weight distribution were determined by gel permeation chromatography (GPC) using poly(ethylene glycol) standard. Poly(N-acryloxysuccinimide) with a target N = 100 and N = 180 were prepared similarly: N = 50, Mn = 6.1 kDa, ĐM = 1.18; N = 100, Mn = 9.2 kDa, ĐM = 1.18; N = 180, Mn = 14.5 kDa, ĐM = 1.25. The removal of trithiocarbonate chain end from polymers was achieved via radical induced reduction following a previous report with minor modifications.57 Poly(N-acryloxysuccinimide) (4.8 g, N = 50), tris(trimethylsilyl)silane (TTMSS, 1.45 g, 10 equiv per polymer chain), and AIBN (96 mg, 1 equiv per polymer chain) were dissolved in DMF (10 mL) in a 50 mL G

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ACS Central Science spectroscopy. The absorption of RB is pH dependent, and therefore all the measurements were carried out at pH 4.2 in citric acid−sodium phosphate buffer (C−P buffer). This buffer also contains 2 M NaCl to prevent phase separation. Polyanions and polycations were separately dissolved at a concentration of 8 wt % in C−P buffer (pH 4.2). Polyelectrolytes were mixed at a 1:1 molar ratio and an overall concentration of 5, 10, 20, and 30 mM (relative to the repeat unit) in a total volume of 0.8 mL in C−P buffer (pH 4.2). The absorbance at 566 nm was plotted versus the concentration to obtain the standard calibration curve. 4.C. Preparation of Polyelectrolyte Complexes. Stock solutions of polyelectrolytes were first prepared separately at a concentration of 8 wt % in Milli-Q water, and the pH was adjusted to 4.2 using 1 M HCl, where both polyelectrolytes are in their fully charged state. The polyelectrolyte solutions were then mixed with a predetermined amount (0.1 or 0.5 equiv to side-chain sulfide on polyelectrolyte) of hydrogen peroxide (30%) at 37 °C for 30 min to oxidize the sulfide groups at different extents. The desired amounts of polyelectrolyte stock solutions, 5 M NaCl solution, and Milli-Q water were mixed to a total volume of 0.8 mL in 1.5 mL Eppendorf tubes and vortexed for 30 s upon mixing. Polyelectrolytes were mixed at equal molar ratio and a total concentration of 0.1 M. The mixtures were left at room temperature for 24 h to equilibrate, and then centrifuged at 1000g for 5 min. The mixtures were then equilibrated at room temperature for another 2 days before measurement of polymer concentrations. 4.D. Analysis of the Separated Phase. The volume of each phase in the phase-separated mixtures was measured by a calibrated pipet. The solution phase was diluted in C−P buffer (pH 4.2) before measurement of polymer concentration based on the calibration curve of RB absorption at 566 nm. The coacervate phase was lyophilized and redissolved in 1 mL of C−P buffer (pH 4.2), and the polymer concentration in the coacervate phase was quantified using the calibration curve. Three independent experimental replicates were used for all experiments.

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ACKNOWLEDGMENTS

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REFERENCES

We acknowledge the seed funding from the Bio-X program at Stanford University for supporting part of this work. J.Q. acknowledges support from the 3M Non-Tenured Faculty Award and the Hellman Scholar Award. We thank Dr. Ali Salehi and Prof. Ronald Larson (University of Michigan) for generously sharing their code and expertise for treatment of ion-binding effects within our theory. We thank Prof. E. Appel and D. Chan for the use of their GPC, and Dr. F. Liu for helpful discussions.

(1) Bungenberg de Jong, H. G.; Kruyt, H. R. Coacervation (partial miscibility in colloid systems). Proc. K. Ned. Akad. Wet 1929, 32, 849−855. (2) Black, K. A.; Priftis, D.; Perry, S. L.; Yip, J.; Byun, W. Y.; Tirrell, M. Protein encapsulation via polypeptide complex coacervation. ACS Macro Lett. 2014, 3, 1088−1091. (3) Johnson, N. R.; Wang, Y. Coacervate delivery systems for proteins and small molecule drugs. Expert Opin. Drug Delivery 2014, 11, 1829−1832. (4) Köse, M. D.; Bayraktar, O.; Ö zge, K. H. In Design and Development of New Nanocarriers; Elsevier, 2018; pp 475−507. DOI: 10.1016/b978-0-12-813627-0.00013-2. (5) Blocher, W. C.; Perry, S. L. Complex coacervate-based materials for biomedicine. Wiley Interdisciplinary Reviews: Nanomedicine and Nanobiotechnology 2017, 9, 76−78. (6) McCall, P. M.; Srivastava, S.; Perry, S. L.; Kovar, D. R.; Gardel, M. L.; Tirrell, M. V. Partitioning and enhanced self-assembly of actin in polypeptide coacervates. Biophys. J. 2018, 114, 1636−1645. (7) Stewart, R. J.; Wang, C. S.; Shao, H. Complex coacervates as a foundation for synthetic underwater adhesives. Adv. Colloid Interface Sci. 2011, 167, 85−93. (8) Brangwynne, C. P.; Eckmann, C. R.; Courson, D. S.; Rybarska, A.; Hoege, C.; Gharakhani, J.; Julicher, F.; Hyman, A. A. Germline P granules are liquid droplets that localize by controlled dissolution/ condensation. Science 2009, 324, 1729−1732. (9) Aumiller, W. M.; Keating, C. D. Phosphorylation-mediated RNA/peptide complex coacervation as a model for intracellular liquid organelles. Nat. Chem. 2016, 8, 129−137. (10) Venkatesh, S.; Workman, J. L. Histone exchange, chromatin structure and the regulation of transcription. Nat. Rev. Mol. Cell Biol. 2015, 16, 178−189. (11) Du, M.; Chen, Z. J. DNA-induced liquid phase condensation of cGAS activates innate immune signaling. Science 2018, 361, 704−709. (12) Zhao, H.; Sun, C.; Stewart, R. J.; Waite, J. H. Cement proteins of the tube-building polychaete Phragmatopoma californica. J. Biol. Chem. 2005, 280, 42938−42944. (13) Sing, C. E. Development of the modern theory of polymeric complex coacervation. Adv. Colloid Interface Sci. 2017, 239, 2−16. (14) Spruijt, E.; Westphal, A. H.; Borst, J. W.; Stuart, M. A. C.; van der Gucht, J. Binodal compositions of polyelectrolyte complexes. Macromolecules 2010, 43, 6476−6484. (15) Fu, J.; Fares, H. M.; Schlenoff, J. B. Ion-pairing strength in polyelectrolyte complexes. Macromolecules 2017, 50, 1066−1074. (16) Perry, S. L.; Leon, L.; Hoffmann, K. Q.; Kade, M. J.; Priftis, D.; Black, K. A.; Wong, D.; Klein, R. A.; Pierce, C. F.; Margossian, K. O.; Whitmer, J. K.; Qin, J.; De Pablo, J. J.; Tirrell, M. Chirality-selected phase behaviour in ionic polypeptide complexes. Nat. Commun. 2015, 6, 6052. (17) Chang, L.-W.; Lytle, T. K.; Radhakrishna, M.; Madinya, J. J.; Vélez, J.; Sing, C. E.; Perry, S. L. Sequence and entropy-based control of complex coacervates. Nat. Commun. 2017, 8, 1273. (18) Perry, S. L.; Li, Y.; Priftis, D.; Leon, L.; Tirrell, M. The effect of salt on the complex coacervation of vinyl polyelectrolytes. Polymers 2014, 6, 1756−1772.

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acscentsci.8b00964. Additional experimental details and figures including synthetic procedures for small molecules and polymers, NMR spectroscopy, and UV−vis spectroscopy (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. ORCID

Jian Qin: 0000-0001-6271-068X Yan Xia: 0000-0002-5298-748X Author Contributions ∥

J.L. and S.F. contributed equally to this work.

Notes

The authors declare no competing financial interest. H

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(42) Fiorucci, S.; Zacharias, M. Prediction of Protein-Protein Interaction Sites Using Electrostatic Desolvation Profiles. Biophys. J. 2010, 98, 1921−1930. (43) Kastritis, P. L.; Bonvin, A. M. J. J. On the binding affinity of macromolecular interactions: daring to ask why proteins interact. J. R. Soc., Interface 2013, 10, 20120835−20120835. (44) Zhou, H.-X.; Pang, X. Electrostatic interactions in protein structure, folding, binding, and condensation. Chem. Rev. 2018, 118, 1691−1741. (45) Chen, S.; Itoh, Y.; Masuda, T.; Shimizu, S.; Zhao, J.; Ma, J.; Nakamura, S.; Okuro, K.; Noguchi, H.; Uosaki, K.; Aida, T. Subnanoscale hydrophobic modulation of salt bridges in aqueous media. Science 2015, 348, 555−559. (46) Chorny, I.; Dill, K. A.; Jacobson, M. P. Surfaces affect ion pairing. J. Phys. Chem. B 2005, 109, 24056−24060. (47) Venkateshwaran, V.; Vembanur, S.; Garde, S. Water-mediated ion-ion interactions are enhanced at the water vapor-liquid interface. Proc. Natl. Acad. Sci. U. S. A. 2014, 111, 8729−8734. (48) Sadman, K.; Wang, Q.; Chen, Y.; Keshavarz, B.; Jiang, Z.; Shull, K. R. Influence of hydrophobicity on polyelectrolyte complexation. Macromolecules 2017, 50, 9417−9426. (49) Hunt, J. N.; Feldman, K. E.; Lynd, N. A.; Deek, J.; Campos, L. M.; Spruell, J. M.; Hernandez, B. M.; Kramer, E. J.; Hawker, C. J. Tunable, high modulus hydrogels driven by ionic coacervation. Adv. Mater. 2011, 23, 2327−2331. (50) Krogstad, D. V.; Lynd, N. A.; Choi, S.-H.; Spruell, J. M.; Hawker, C. J.; Kramer, E. J.; Tirrell, M. V. Effects of polymer and salt concentration on the structure and properties of triblock copolymer coacervate hydrogels. Macromolecules 2013, 46, 1512−1518. (51) Krogstad, D. V.; Lynd, N. A.; Miyajima, D.; Gopez, J.; Hawker, C. J.; Kramer, E. J.; Tirrell, M. V. Structural evolution of polyelectrolyte complex core micelles and ordered-phase bulk materials. Macromolecules 2014, 47, 8026−8032. (52) Friedowitz, S.; Salehi, A.; Larson, R. G.; Qin, J. Role of electrostatic correlations in polyelectrolyte charge association. J. Chem. Phys. 2018, 149, 163335. (53) Chu, J.-W.; Trout, B. L. On the mechanisms of oxidation of organic sulfides by H2O2 in aqueous solutions. J. Am. Chem. Soc. 2004, 126, 900−908. (54) Priftis, D.; Tirrell, M. Phase behaviour and complex coacervation of aqueous polypeptide solutions. Soft Matter 2012, 8, 9396−9405. (55) Semenov, A. N.; Rubinstein, M. Thermoreversible gelation in solutions of associative polymers. 1. Statics. Macromolecules 1998, 31, 1373−1385. (56) Bucur, C. B.; Sui, Z.; Schlenoff, J. B. Ideal mixing in polyelectrolyte complexes and multilayers: entropy driven assembly. J. Am. Chem. Soc. 2006, 128, 13690−13691. (57) Chong, Y. K.; Moad, G.; Rizzardo, E.; Thang, S. H. Thiocarbonylthio end group removal from RAFT-synthesized polymers by radical-induced reduction. Macromolecules 2007, 40, 4446−4455.

(19) Overbeek, J. T. G.; Voorn, M. J. hase separation in polyelectrolyte solutions. Theory of complex coacervation. J. Cell. Comp. Physiol. 1957, 49, 7−26. (20) Srivastava, S.; Tirrell, M. V. In Advances in Chemical Physics; John Wiley & Sons, Inc., 2016; pp 499−544. DOI: 10.1002/ 9781119290971.ch7. (21) Muthukumar, M.; Hua, J.; Kundagrami, A. Charge regularization in phase separating polyelectrolyte solutions. J. Chem. Phys. 2010, 132, 084901. (22) Jha, P.; Desai, P.; Li, J.; Larson, R. pH and salt effects on the associative phase separation of oppositely charged polyelectrolytes. Polymers 2014, 6, 1414−1436. (23) Muthukumar, M. Theory of counter-ion condensation on flexible polyelectrolytes: adsorption mechanism. J. Chem. Phys. 2004, 120, 9343−9350. (24) Kundagrami, A.; Muthukumar, M. Theory of competitive counterion adsorption on flexible polyelectrolytes: divalent salts. J. Chem. Phys. 2008, 128, 244901. (25) Adhikari, S.; Leaf, M. A.; Muthukumar, M. Polyelectrolyte complex coacervation by electrostatic dipolar interactions. J. Chem. Phys. 2018, 149, 163308. (26) Zhang, P.; Alsaifi, N. M.; Wu, J.; Wang, Z.-G. Salting-out and salting-in of polyelectrolyte solutions: a liquid-state theory study. Macromolecules 2016, 49, 9720−9730. (27) Zhang, P.; Shen, K.; Alsaifi, N. M.; Wang, Z.-G. Salt partitioning in complex coacervation of symmetric polyelectrolytes. Macromolecules 2018, 51, 5586−5593. (28) Qin, J.; de Pablo, J. J. Criticality and connectivity in macromolecular charge complexation. Macromolecules 2016, 49, 8789−8800. (29) Shen, K.; Wang, Z.-G. Electrostatic correlations and the polyelectrolyte self energy. J. Chem. Phys. 2017, 146, 084901. (30) Ermoshkin, A. V.; Kudlay, A. N.; de la Cruz, M. O. Thermoreversible crosslinking of polyelectrolyte chains. J. Chem. Phys. 2004, 120, 11930−11940. (31) Kudlay, A.; Ermoshkin, A. V.; Olvera de la Cruz, M. Complexation of oppositely charged polyelectrolytes: effect of ion pair formation. Macromolecules 2004, 37, 9231−9241. (32) Lytle, T. K.; Sing, C. E. Transfer matrix theory of polymer complex coacervation. Soft Matter 2017, 13, 7001−7012. (33) Salehi, A.; Larson, R. G. A molecular thermodynamic model of complexation in mixtures of oppositely charged polyelectrolytes with explicit account of charge association/dissociation. Macromolecules 2016, 49, 9706−9719. (34) Delaney, K. T.; Fredrickson, G. H. Theory of polyelectrolyte complexationcomplex coacervates are self-coacervates. J. Chem. Phys. 2017, 146, 224902. (35) Radhakrishna, M.; Basu, K.; Liu, Y.; Shamsi, R.; Perry, S. L.; Sing, C. E. Molecular connectivity and correlation effects on polymer coacervation. Macromolecules 2017, 50, 3030−3037. (36) Lytle, T. K.; Salazar, A. J.; Sing, C. E. Interfacial properties of polymeric complex coacervates from simulation and theory. J. Chem. Phys. 2018, 149, 163315. (37) Li, L.; Srivastava, S.; Andreev, M.; Marciel, A. B.; de Pablo, J. J.; Tirrell, M. V. Phase behavior and salt partitioning in polyelectrolyte complex coacervates. Macromolecules 2018, 51, 2988−2995. (38) Audus, D. J.; Gopez, J. D.; Krogstad, D. V.; Lynd, N. A.; Kramer, E. J.; Hawker, C. J.; Fredrickson, G. H. Phase behavior of electrostatically complexed polyelectrolyte gels using an embedded fluctuation model. Soft Matter 2015, 11, 1214−1225. (39) Priftis, D.; Xia, X.; Margossian, K. O.; Perry, S. L.; Leon, L.; Qin, J.; de Pablo, J. J.; Tirrell, M. Ternary, tunable polyelectrolyte complex fluids driven by complex coacervation. Macromolecules 2014, 47, 3076−3085. (40) Schellman, J. A. The application of the Bjerrum ion association theory to the binding of anions by proteins. J. Phys. Chem. 1953, 57, 472−475. (41) Bogan, A. A.; Thorn, K. S. Anatomy of hot spots in protein interfaces. J. Mol. Biol. 1998, 280, 1−9. I

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