Ion-Pairing Strength in Polyelectrolyte Complexes - Macromolecules

Jan 26, 2017 - (1)Complexation proceeds almost athermally, which demonstrates the importance of the gain in entropy of counterions A– and M+ in driv...
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Ion-Pairing Strength in Polyelectrolyte Complexes Jingcheng Fu, Hadi M. Fares, and Joseph B. Schlenoff* Department of Chemistry and Biochemistry, The Florida State University, Tallahassee, Florida 32306, United States S Supporting Information *

ABSTRACT: Polyelectrolyte complexes, PECs, are spontaneously formed blends of polyelectrolytes bearing positive, Pol+, and negative, Pol−, repeat units. Many interesting PEC morphologies have been observed, ranging from dense precipitates to liquidlike coacervates to quasi-stable nanoparticles, depending on the identity of the polymers and the preparation conditions. While the number of polyelectrolytes available to synthesize these materials is large and increasing, the corresponding number of Pol+/Pol− combinations is vast. This work quantitatively compares the binding strengths between a selection of positive and negative polyelectrolytes by evaluating the extent to which ion pairs between them are broken by a common salt, KBr. Comparison of association constants or Gibbs free energies between different classes of ionic functionality reveals that more “hydrophilic” PECs are more weakly associated, small primary amines bind strongly, carboxylates bind weakly, and aromatic sulfonates interact more strongly than aliphatic ones. The use of “charge density” to predict binding strength is shown not to be justified. Ion diffusion coefficients through PECs also approximately follow water content and are inversely related to interaction strength.

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INTRODUCTION Repeat units on oppositely charged polyelectrolytes associate when solutions of these water-soluble polymers are mixed.1 Ion pairing between positive, Pol+, and negative, Pol− units, represented by eq 1, leads to a variety of interesting morphologies, ranging from dense polyelectrolyte complexes2−9 including multilayers10,11 to liquidlike coacervates12−18 to nanoparticulate dispersions19−26 (some stabilized by a neutral shell27−30), depending on the mixing conditions. Pol+A− + Pol−M+ ⇌ Pol+Pol− + A aq − + M aq +

categorized polycarboxylates as weak/labile complex formers, while sulfonates were said to yield stronger, nonlabile PECs.20,21 Van der Gucht et al. attempted to rank complexes by observing the minimum amount of salt needed to dissociate them completely.14 The interaction strength between Pol+ and Pol− is directly probed by the ability of salt MA added to break ion pairs, which is the reverse of eq 1.36 The challenge in making reliable, quantitative measurements of interaction strength is how to provide samples and methods to measure this equilibrium. The entry of ions and their waters of solvation into PEC causes swelling. We observed large differences in the salt-induced swelling of three combinations of Pol+Pol− in their ultrathin multilayer formats.37 In more quantitative approaches, we subsequently employed spectroscopic methods to track the composition of thin films of PEC as a function of the solution concentration of salt.38 More recently, we have exploited the salt−water plasticization of PECs (“saloplasticity”) to extrude dense shapes suitable for many types of measurements,39 including ion equilibria.40 In the present study, several combinations of Pol+ and Pol− have been extruded to yield dense samples of PEC for ion equilibrium studies. The results reveal several trends, some of which are counterintuitive, in polyelectrolyte association strength, a fundamental parameter needed to construct and understand PECs of various morphologies.

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Complexation proceeds almost athermally, which demonstrates the importance of the gain in entropy of counterions A− and M + in driving eq 1 to the right. 2,31,32 Because all polyelectrolytes bear counterions, mixing at the molecular level to give uniform blends33 is a common property of polyelectrolyte complexation. Since the first report of synthetic polyelectrolytes,8 the library of potential Pol+/Pol− pairs has steadily expanded. Charges on most reported polyanions are carried by sulfonates or carboxylates whereas the repeat unit on polycations is usually an amine or ammonium functionality. Biological or biologically derived polymers (such as modified celluloses34) add an almost limitless variety of charged macromolecules to the toolbox.35 In spite of the number of and growing interest in polyelectrolyte complexes, little is known concerning quantitative comparisons between specific Pol+/Pol− pairs in the PEC “interactosome”. Qualitatively, it is known that salts of poly(meth)acrylic acids tend to form weaker, hydrated complexes, which is why they are frequently employed in the study of coacervates.13,17 Notable early work by the Moscow State group comparing labile versus nonlabile combinations of polyelectrolytes also © XXXX American Chemical Society

Received: November 11, 2016 Revised: January 10, 2017

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Polymer Stoichiometry. Scintillation counting was performed directly on PEC labeled with 22Na using 3.8 cm diameter, 3 mm thick plastic scintillator disks (SCSN-81, Kuraray America) which were sitting on the window of a 5 cm diameter end-on photomultiplier tube (PMT, RCA 8850) maintained at 2130 V with a high voltage supply in a dark box. A drop of immersion oil was sandwiched between the plastic and the PMT window to ensure good optical contact. While the γ radiation from 22Na is not appreciably absorbed by PEC, the βemissions from 35S have a penetration length of about 50 μm. Thus, the 35SO42− had to be extracted from the PEC before counting in liquid scintillator. The PMT was also used for liquid scintillation counting. Counts were recorded with a Philips PM6654C frequency counter interfaced with a computer running LabView software. Counts were collected over a gate time of 10 s with the pulse threshold of −20 mV. The total number of counts for each sample ranged between 300 and 2 500 000 with respective counting errors of 5.96% and 0.06%. As some samples disintegrated when immersed in water (PDDPC-PVS, PDDPC-PAA, PVTAC-PAA, and PDADMA-PVS), they were rinsed and labeled in solutions of 1:6 water:ethanol. They were then washed in solutions of unlabeled 10−2 M NaCl in 1:6 water:ethanol to remove the radiolabel. Sodium-22 (Negative Extrinsic Sites) Labeling. 22NaCl was used to quantify the total amount of negative extrinsic sites (PSSNa) by labeling with a 10−2 M solution with a specific activity of 0.05 Ci mol−1. The solution was prepared by diluting 263 μL of the stock solution in a total volume of 50 mL 10−2 M “cold” (nonradioactive) NaCl. This specific activity yielded estimates of 0.5% for counting precision. Extruded complex was soaked in “cold” (nonradioactive) NaCl for 18 h and then in water for 6 h to remove any excess salt. This step ensured that the sodium counterion occupied all negative extrinsic sites in the PEC pieces. The pieces were then soaked in the “hot” 22Na solution between 1 and 24 h. Each piece of PEC was subsequently soaked for an extra amount of time (the same used in the first soaking) in the radiolabel to verify that the exchange had reached completion. Labeled samples were rinsed briefly with water to remove excess 22Na solution from the surface and then stored in water from 30 min to 3 h until the count rate was stable to ensure the removal of excess/ noncounterion 22Na from within the complex (such as any 22Na that might be in pores). Next, counting was performed for 15 min. To convert counts to mol m−2, a calibration curve was built by dispensing 1−5 μL of the “hot” solution on the plastic scintillator, covering a silicon wafer, and counting. At the end of counting, PEC pieces were soaked successively in two fresh aliquots of “cold” 0.01 M NaCl for the same time used in radiolabeling to exchange out the radiolabel. After washing with water, the pieces were air-dried and then oven-dried at 120 °C for 18 h. The percent of negative extrinsic sites was obtained by dividing the number of moles of radiolabel by the number of moles of PEC calculated from the dry weight. Sulfate-35 (Positive Extrinsic Sites) Labeling. 35S-labeled sulfate was used to label positive extrinsic sites using a 10−2 M Na235SO4 solution with a specific activity of 0.1 Ci mol−1. 65 μL of the “hot” stock solution was diluted in 49.9 mL of “cold” 10−2 M Na2SO4. As with sodium labeling, all PEC pieces were soaked in 10−2 M “cold” sulfate for 18 h and then washed with water to replace all ions with sulfate. 35S was counted in a Liquid Scintillation Cocktail (LSC). First, all samples were soaked for 48 h in the “hot” 35S-labeled sulfate solution. This was followed by washing and soaking the pieces in water for 4 h. The complexes were then air-dried for 2 h and soaked in 2 mL of 10−2 M “cold” Na2SO4 for 72 h to extract the radiolabeled sulfate. For the counting, 500 μL of the extracted solution (the supernate above the PEC) was added to 6 mL of LSC in a glass scintillation vial, shaken vigorously to disperse the “hot” solution, and counted for 15 min after the disappearance of bubbles. Five different samples were counted again at 92 h of extraction to ensure that 72 h was enough. As with the Na+ experiment, all samples were oven-dried at 120 °C to obtain dry weights. A calibration curve was built by dispensing 1−5 μL of the labeling solution in 6 mL of LSC with the addition of 500 μL of “cold” 10−2 M sulfate to ensure the same environment as the counting of the samples.

EXPERIMENTAL SECTION

Materials. Poly(diallyldimethylammonium chloride) (PDADMA, molar mass 400 000−500 000), poly(4-styrenesulfonic acid) (PSS, molar mass 75 000), poly(vinylsulfonic acid, sodium salt) solution (PVS, 25 wt % in water), poly(acrylic acid) (PAA, molar mass 240 000), and sodium chloride (99.5%) were used as received from Sigma-Aldrich. Poly(N,N-dimethyl-3,5-dimethylene piperidinium chloride) (PDDPC, molar mass 200 000−300 000, 20% solids in water), poly(vinylbenzyltrimethylammonium chloride) (PVTAC, 26.9 wt % solids in water, molar mass 100 000), and poly(2-acrylamido-2methyl-1-propanesulfonic acid) (PAMPS) were from Scientific Polymer Products. Poly(allylamine) (molar mass 15 000, Polysciences, Inc.), polyvinylamine (PVA, BASF Lupamin 9095 molar mass 205 000), and potassium thiocyanate (KSCN) from Fisher Scientific were used as received. Sodium-22 was received from PerkinElmer as 22 NaCl (half-life 950 days, positron, γ emitter, 1.275 MeV) with a specific activity of 456 mCi mg−1. The stock solution of sodium was 1 mL in water. Sulfur-35 radionuclide was purchased from PerkinElmer as Na235SO4 in water (half-life 87.4 days, β emitter, Emax = 167 keV). The stock solution was used as supplied1 mCi in 1 mL of water with a specific activity equal to 1494 Ci mmol−1. EcoLite(+) Liquid Scintillation Cocktail was used as received from MP Biomedicals. All solutions were prepared using 18 MΩ deionized water (Barnstead, Epure). All polyelectrolyte solutions were 0.125 M based on the repeat unit and were adjusted to pH 7 before use by adding NaOH or HCl. Polymer Complexation and Extrusion. Equal volumes (molar ratio 1:1) of polycation and polyanion solution were mixed simultaneously for 30 min under stirred conditions at room temperature. A selection of five polycations and four polyanions yielded a total of 20 Pol+Pol− possible combinations. Some complexations were facilitated by the addition of salt. The type and concentration of salt were optimized by trial and error for each combination, as summarized in Table S1 of the Supporting Information. Complexes were then chopped into chunks between 5 and 10 mm across and then annealed in solution for 24 h under conditions that were optimized, also summarized in Table S1. The purpose of annealing was to consolidate the chunks of precipitate into a rubbery mass that could be extruded into filaments. Samples were transferred directly from annealing solutions into a Model LE-075 laboratory extruder (Custom Scientific Instruments). The rotor/ header temperatures were adjusted for each polymer complex (Table S1) with a gap space of 3.8 mm. All the processing information for individual complexes is listed in the Supporting Information. Doping Level Measurements. A Thermo Orion 3 Star 4-probe conductivity meter fitted with a cell controlled to 25 ± 0.1 °C was standardized with NaCl solutions. Extruded PECs, exPECs, were soaked in copious water to extract ions left over from extrusion, cut into approximately 1 cm rods, immersed separately into KBr at different concentrations at room temperature (23 ± 2 °C), and allowed to dope to equilibrium for at least 24 h. exPECs were then wiped and dropped into 100.00 mL of water with a stir bar in the conductivity cell. Conductivities were recorded every 15 s for at least 90 min as samples undoped. After undoping, all the exPECs were dried at 110 °C for 12 h to obtain the dry mass. To obtain water content, dry exPECs were soaked in water for 2.5 h at rt and then weighed. Thermogravimetric Analysis. TGA was performed to determine the decomposition temperature of PECs. Samples were first soaked in water to remove salt, and then they were allowed to dry under ambient conditions. Samples were heated under Ar with a temperature ramp of 20 °C min−1 to 110 °C and held at this temperature for 20 min to remove water. Heating was then resumed to 800 °C at a rate of 10 °C min−1. Electron Microscopy. Samples of hydrated PEC were cut with a razor blade and affixed to a double-side adhesive carbon tape. They were coated with a 4 nm layer of iridium using a Cressington HR 208 sputter coater. Imaging was done using an FEI Nova 400 NanoSEM with an Everhart-Thornley detector (ETD) at an acceleration voltage of 5 kV. B

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“annealing” solutions provided rubbery PEC which could be extruded under conditions summarized in Table S1. Some of the coacervates could not be sufficiently dehydrated to process further. During extrusion, PECs were maintained wet and heated to temperatures that were presumably above their glass transition temperature. The hottest zone was at the exit nozzle of the extruder, which was maintained between 75 and 105 °C, with higher temperatures employed for the glassier PECs. Extruded PECs are termed exPECs. To verify that the highest processing temperatures did not induce degradation of blends, TGA was performed on all PECs. Figure 1 shows an example of PDADMA-PSS heated to 800

RESULTS AND DISCUSSION Polyelectrolyte Complex Combinations. The polymers selected for complex formation, commercially available representatives of common positive and negative repeat units, are summarized in Scheme 1. These allowed comparisons of Scheme 1. Structures of Polyelectrolytes Employeda

a

Cations: poly(N,N-dimethyl-3,5-dimethylene piperidinium) (PDDP); poly(allylamine) (PAH); poly(vinylbenzyltrimethylammonium) (PVTA); poly(diallyldimethylammonium) (PDADMA); poly(vinylamine) (PVA). Anions: poly(acrylamido-2-methylpropanesulfonate) (PAMPS); poly(vinylsulfonate) (PVS); poly(acrylic acid) (PAA); poly(styrenesulfonate) (PSS). Counterions for the as-supplied materials were chloride or sodium.

Figure 1. Thermogravimetric analysis of PDADMA-PSS exPEC under Ar.

°C. This PEC is stable up to about 350 °C, whereupon rapid decomposition occurred (Figure 1). Figure S1 in the Supporting Information provides individual TGA results for each PEC. The temperature for 10% weight loss is summarized in Table 1.

aromatic versus aliphatic, carboxylate compared to sulfonate, alkylammonium with amine and a range of charge densities (defined as either the number of backbone carbons per charged unit or the repeat unit volume). We initially attempted to order the strengths of PEC association by trying to find the minimum concentration of KBr needed to dissolve them using turbidimetry and observation.14 Unfortunately, it proved difficult to tell when a PEC was truly dissolved. We thus proceeded to doping extruded samples which had yielded unambiguous data in prior work.40 As a practical matter, each Pol+Pol− combination required optimization of salt conditions for precipitation and extrusion in order to approach fully dense, stoichiometric, uniform PEC. Simultaneous mixing of components was more likely to yield stoichiometric PECs, as shown by our previous experience39,41 and by earlier reports that PEC composition is influenced by the order of mixing.42,43 Differences in association affinities between combinations of Pol+ and Pol− were immediately apparent on precipitation. Problems were encountered at both ends of the spectrum of association strength. Weakly interacting systems, such as those employing PAA, spontaneously formed soft, liquidlike precipitates that were identified as coacervates, which could not easily be extruded or handled. Strongly interacting pairs tended to produce finely divided particles which did not agglomerate into larger chunks, making them difficult to feed into the extruder. Table S1 summarizes the conditions used to produce tractable, extrudable material. Excessively soft PECs were hardened by extracting water from them using organic solvent. For example, ethanol, a nonsolvent for PECs, mixed with water partially dehydrated PDDPC/PVS and PDDPC/PAA coacervates. At the other extreme, 3.5 M KBr was able to plasticize strong PECs such as PSS/PVA and PSS/PAH, resulting in aggregation and fusion of the fine particle precipitate. Treatment by these

Table 1. Temperature (°C) for 10% Loss in Dry Weight of Complexes PDDPC PVTAC PDADMA PAH PVA

PSS

PVS

PAMPS

PAA

367 363 369 305 326

312 310 319 334 330

310 298 312 300

219 200 230 230

All sulfonate PECs were stable up to about 300 °C, whereas PECs containing acrylic acid decomposed some 100 °C lower. Thermal decomposition reactions were not investigated further but are discussed in the literature and are believed to occur at 300−350 °C for −SO3−,44,45 200−280 °C for amine,46 and around 300 °C for quaternary ammonium,47 with dehydration and cross-linking48 around 175 °C for carboxylates.49 PECs were stored dry in ambient after extrusion into fibers ca. 1 mm in diameter. Samples of fiber were rehydrated with water or the ethanol/water combination that had been used to anneal them then cut with a razor blade. Scanning electron microscopy of these cross sections showed most PECs were dense/space filling. Pores were observed (Figure S2) in PDDPC-PSS, PAH-PSS, PDADMA-PSS and, to a lesser extent, PAH-PAA and PVA-PSS. This porosity was judged to be minor. Some complexes remained viscous liquids, even in the absence of salt, and thus could not be formed into shapes for measurements. Those combinations which formed “spontaneous coacervates” are identified in Table 2. PAA and PVS were C

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Macromolecules Table 2. Stoichiometry, Equilibrium Constant, and Calculated ΔG°a for Complexes in KBra PSS

PDDPC PVTAC PDADMA PAH PVA

molar ratio of Pol+:Pol− 1.071 1.048 1.032 1.060 0.987

PVS

PAMPS

Ka

ΔGa° (kJ mol−1)

molar ratio of Pol+:Pol−

ΔGa° (kJ mol−1)

Ka

0.79 1.48 2.42 12.92 17.55

0.57 −0.97 −2.19 −6.34 −7.10

1.011 0.999* 1.006 1.011 0.997

C 1.85* C 4.10 2.41

−1.52* −3.50 −2.18

molar ratio of Pol+:Pol− 1.047* 1.023 1.039 1.031*

PAA

Ka

ΔGa° (kJ mol−1)

molar ratio of Pol+:Pol−

Ka

ΔG°a (kJ mol−1)

2.97* 0.57 0.28 3.88*

−2.7* 1.40 3.14 −3.36*

1.001 1.001 1.037 1.002

C C 0.09 2.53

6.03 −2.30

C = coacervate-like complex. The numbers followed by an asterisk are the data from three “weak” samples. Errors for ratio are ±0.005, for Ka ± 5%, and for ΔGa° ±0.2 kJ mol−1. a

noted for this property. These are both “high charge density” materials, the former a well-hydrated weak polyacid which is known for its propensity to produce coacervates with polycations and the latter a strong sulfonic acid polyelectrolyte. Doping and Pol+Pol− Association Energies. Pol+Pol− pairs were challenged by immersing PEC into solutions of salt. Under the chemical potential (concentration) of this salt, counterions are “doped” into the PEC until equilibrium is achieved.38 The doping follows a Hofmeister series,50 where less hydrated anions and cations dope the PEC more efficiently.51,52 For a comparison of various Pol+Pol− pairs a “universal” salt is needed, which is strong enough to dope the strong PECs but not too strong to excessively dope and decompose the weaker PECs. KBr, employed for this purpose, dopes PECs as follows: Pol+Pol−PEC + Br −aq + K +aq ⇌ Pol+Br −PEC + Pol−K+PEC

Figure 2. Concentration of KBr released versus time after immersion of doped exPEC in water at 25 °C for PDADMA-PSS complex. Samples were first doped to equilibrium for 24 h in 0.10, 0.40, 0.25, 0.60, and 0.80 activity KBr at room temperature. Concentration was obtained directly from conductivity every 15 s. The plateau conductivity indicates release of all KBr, which was used to calculate the original doping level.

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The term “intrinsic site” is used to describe the site in a PEC where the Pol+ is compensated by the Pol−, while “extrinsic site” describes when polyelectrolytes are compensated with a salt counterion (either K+ or Br−). Equilibrium doping level y represents the fraction of extrinsic sites in the PEC. An association constant, Ka, the inverse of equilibrium (2), is defined as the following:38 Ka =

(1 − y)aKBr 2 y2

→

aKBr 2 y2

then warmed at 60 °C for 24 h to accelerate undoping. Conductivities of these solutions were measured after the samples were cooled to 25.0 °C. This heating and cooling process was repeated until no change in conductivity was obtained which was considered the final plateau where all KBr had been extracted. Plateau conductivities were then converted to amounts of KBr released and compared to the dry weight of salt-free exPECs to calculate the doping level. Typical data for doping level vs salt activity for five exPECs made from PSS as polyanion are presented in Figure 3A, and exPECs containing PAH are shown in Figure 3B. Doping behavior of all 14 combinations of Pol+ and Pol− is shown in Figure S4. Association constants calculated from the slopes of the doping responses and eq 3, and corresponding Gibbs free energies of association, ΔG°a , using ΔG°a = −RT ln Ka, are listed in Table 2. Before comparisons between PECs could be made, we needed to verify that the stoichiometry was close to 1:1. Prior work on PECs does not always include a check of stoichiometry, usually assumed to be 1:1, but there are many examples where the ratio of positive to negative repeat units is not 1.00. Nonstoichiometry requires charge to be balanced by counterions. For the combinations studied here, the presence of Na+ in undoped PEC means there is an excess of PSS. Likewise for PDADMA and SO42−. These counterion-compensated “extrinsic” sites were determined using radiochemical methods. The net counterion charge in a PEC is calculated as [Na+] − (2[SO42−]), which represents the net excess of one of the polyelectrolytes. If no net counterion charge is found, the ratio of Pol+/Pol− is 1.00. The measured ratio of Pol+/Pol− for all exPECs is given in Table 2. The radiochemical method is much

(as y → 0) (3)

where (1 − y) is the fraction of intrinsic sites and aKBr is the activity of the salt KBr. The amount of KBr in doped, equilibrated PECs was determined by releasing the KBr into pure water while measuring the conductivity. The conductivity was translated into concentration with the aid of a series of KBr conductivity standards. Figure 2 shows examples of this spontaneous undoping of PDADMA/PSS exPEC doped with various activities of KBr (converted from [KBr] using activity coefficients). Kinetic data were deduced from the rate of ion release. Since the volume ratio of bulk water (100 cm3) to exPEC volume (around 0.01 cm3) was high, it was assumed that all the KBr inside the exPECs was eventually released into water. Similar data for 13 other exPECs are shown in Figure S3. Four combinations (PDDPC-PVS, PDDPC-PAA, PVTACPAA, and PDADMA-PVS) which required partial dehydration with ethanol to extrude became too sticky and soft when they were soaked into water to perform conductivity measurements. Conductivities of most exPECs reached a plateau within 100 min. Three of the most hydrated samples (PDDPC-PAMPS, PAH-PAMPS, and PVTAC-PVS), which showed much slower undoping kinetics, were undoped in water for 100 min at rt and D

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polycations, PVA ≈ PAH > PDADMA > PVTAC > PDDPC. Inspection of Table 2 reveals exceptions. As expected, the weakest couples include PAA. Some of these produced coacervates, which were liquidlike in behavior. The boundary between a coacervate and a complex is not sharp, perhaps defined as a crossing point between storage (G′) and loss (G″) modulus (i.e., coacervate if G″/G′ > 1).54 Coacervation could be broken down into spontaneous coacervation, those Pol+/Pol− combinations or proportions which yielded coacervates without the addition of salt or another stimulus (such as heating or change in pH), and induced coacervates, which needed additional treatment or stimulus, such as the addition of M+A−. It could be predicted that the spontaneous coacervate formers will have the lowest Kas, but this remains to be proven. Table 2 suggests which PECs are the most tractable and useful for experiments to explore the fundamental properties of complexes. The combination of Pol+ and Pol− depends on the property sought. Research on coacervates is best done with weaker complexes, although it is possible to add enough salt to press a “medium” strength complex like PDADMA/PSS into behaving like a coacervate.54 The glassy PAH/PSS is not the best combination to evaluate the substantial effects of ion content on PEC properties, though it is one of the most common in use, perhaps because of influential early experiments of the Strasbourg,10,55 Max Planck,56 and MIT57,58 groups demonstrating the power of the layer-by-layer assembly method. While the mechanical properties of undoped PEC have more to do with water content, PAH/PAA and PDADMA/PSS are “medium” strength combinations providing access to low- and high-salt content materials. Some ideas regarding what is loosely termed “charge density” may be assessed using Table 2, which includes examples of one charge per two, four, and five backbone carbons (linear charge density) and 41 g per mole of charge (“high” volume charge density) to 194 g per mole of charge (“low” volume charge density). From an electrostatics analysis, complexes with the greatest number of charges per backbone carbon or per unit volume should associate more strongly. This is not the case, as PVS, a strong polyelectrolyte, and PAA, a weak polyelectrolyte, both give relatively weak complexes despite only having 2 or 3 carbons per repeat unit. The type of charge appears to be more important than the charge density. For example, carboxylates associate more weakly than sulfonates, and primary amines associate more strongly than quaternary ammoniums. Furthermore, the aromatic sulfonate associates more strongly than the aliphatic one. Cation−π interactions might assist the binding, but this would lead to an enthalpy change (a few kJ mol−1 for aqueous tetramethylammonium interacting with benzene59) which was not detected using calorimetry measure-

Figure 3. (A) Doping level, y, in exPEC versus KBr solution activity of PDDPC-PSS (◆), PAH-PSS (■), PVTAC-PSS (□), PDADMAC-PSS (●), and PVA-PSS (◇). (B) y versus KBr activity for PAH-PAMPA (◇), PAH-PVS (□), PAH-PAA (▲), and PAH-PSS (■).

more sensitive to small deviations from 1.00 ratio than are NMR, FTIR, or elemental analysis. As Table 2 shows, even a ratio of 1.001 (0.1% excess of one polymer) is measurable. From Table 2 it is clear that the worst deviation from equal stoichiometry was 1:1.07 (PDDPC-PSS). Does small ( PVS > PAMPS > PAA, and for the

Table 3. Water Content of Salt-Free PECs in Both Water Weight Percentage and Molar Ratio (nwater/nPEC) after Soaking in H2O for 2.5 ha PSS PDDPC PVTAC PDADMA PAH PVA a

PVS

PAMPS

PAA

wt % H2O

molar ratio

wt % H2O

molar ratio

wt % H2O

molar ratio

wt % H2O

molar ratio

77 36 37 44 47

60 11 10 10 11

52 42 68 30 30

15 11 28 4 4

52 35 43 40

21 11 14 10

68 57 59 53

25 18 16 8

Entries in bold are for combinations that show spontaneous coacervation. E

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using eq 4. An example of such a fit is shown in Figure 4. Fits to undoping kinetics for the other PECs are given in Figure S5.

ments of PDADMA complexing with PSS in KBr.60 It appears that the more “hydrophilic” the repeat unit, the weaker the association if hydrophilicity/phobicity is quantified in terms of number of water molecules per repeat unit.51 These categories of interaction strengths fall in line with deductions concerning carboxylate versus sulfonate made by Kabanov and co-workers some decades ago.61,62 This general categorization would also be important in biomolecular interactions, such as carboxylate groups on aspartate and glutamate forming “salt bridges” with positive amino acids (histidine, lysine, arginine) during protein folding.63 In addition, surfaces presenting sulfonates would interact more strongly with opposite charges than those bearing carboxylates. Qualitative trends in morphology and modulus will be familiar to the experienced PEC researcher. Descriptive terms for strong (“glassy; stiff”), intermediate (“rubbery”), and weak (“soft; viscous; sticky; tacky”) PECs correlate reasonably well with their water content. For example, we were expecting all coacervates to be more hydrated than PDADMA/PSS, our favored PEC, which is fairly stiff (∼10 MPa) when undoped. Table 3 summarizes the water content in terms of wt % and also the number of water molecules per Pol+Pol− repeat unit. Some complexes are much “dryer” than others. For example, PVA/PVS has only 4 molecules per Pol+Pol− while PDDPC/ PSS has 60 waters. In this case the charge density can be inversely correlated with the hydration level, as closely spaced charges should allow less free volume for water when they associate. Our previous analysis predicted a correlation between binding strength and dehydration of the polyelectrolytes on binding.51 Other structures which rely on polyelectrolyte complexation, such as polyion complex micelles30 and coacervates,13 also exhibit decreasing polyelectrolyte binding with increasing salt and hydrophilic content. Removal of water from a PEC by an external osmotic stressing agent causes a strong increase in bulk modulus.64 All mentioned property comparisons are for fully hydrated PECs. Dried PECs are almost exclusively brittle, hard to handle, and unprocessable.2 Ion Diffusion Rates. If ion transport in PECs is related to hopping between Pol+ or Pol− units,38 weaker associations between Pol+ and Pol− should lead to faster ion transport. The rate of ion release shown in Figure 2 provides the opportunity to calculate diffusion coefficients.40 A cylindrical geometry model was used to fit the exPEC undoping data. The fraction of KBr released from the samples f after time t is expressed by65 f=

Mt =1− M∞

∞

∑ n=1

4 −D̅ αn2t / r 2 e αn2

Figure 4. Fraction f of KBr released vs t1/2 from PDADMA-PSS exPEC doped to equilibrium with 0.25 M KBr. The solid curve is a fit according to eq 4 with D̅ = 11 × 10−7 cm2 s−1. As with interaction strengths, strong differences in diffusion coefficient, ranging from 0.7 to 190 × 10−7 cm2 s−1, summarized in Table 3, were apparent with various combinations of Pol+ and Pol−.

Undoping kinetics for three samples that started at y = 0.04 were carried out for 100 min. The plateau conductivity values were determined using the heating method above to obtain M∞ and then f. Table 4. Diffusion Coefficients for Various Combinations of Pol+ and Pol− Having a Doping Level near 0.1a D̅ y=0.1 (×10−7 cm2 s−1)

PSS

PVS

PAMPS

PAA

PDDPC PVTAC PDADMA PAH PVA

9.3 14 11 1.0 7.3

C 3.3* C 0.7 0.7

5.1* 27 190 1.4*

C C 44 7.9

For numbers followed by an asterisk the doping level was 0.04. “C” represents a coacervate.

a

If diffusion were controlled by ion hopping from site to site,38 the diffusion coefficient should increase with doping level. This behavior has been seen before for PSS/PDADMA40 and probably explains the slower diffusion seen for the three PECs doped to y = 0.04. Thus, only PECs doped to the same y should be compared. The overall trend is that the least hydrated, stronger PECs yield lower diffusion coefficients. For example, PAH/PVS and PVA/PVS both had the lowest water content and the slowest diffusion, while well-hydrated PDADMA/PAMPS and PDADMA/PAA showed the highest D̅ , approaching the solution value of 2 × 10−5 cm2 s−1.66 Because diffusion probably relies on coupled segmental motion to generate hopping attempts, like phonons coupled to electrons, it is likely that the more glassy the PEC, the slower the ion transport rate. However, diffusion is a complex process that depends on several factors.

(4)

where Mt is the amount of KBr released from exPECs after t seconds and M∞ is the amount of KBr released from exPECs after infinite time. D̅ is the diffusion coefficient of KBr within the exPEC samples. αn are the roots of the Bessel function of the first kind of zero order, and r is the radius of the cylindrical samples. An assumption was made that all salt was released from the exPECs when conductivity in Figure 2 had reached the plateau. Previous work has demonstrated that D̅ depends on doping level.40 Thus, samples doped to y = 0.1 were selected using the equilibrium doping data of Figure 3 and Figure S3. An exception had to be made for three weakly interacting combinations (PDDPC-PAMPS, PAH-PAMPS, and PVTACPVS) where y = 0.04 for kinetics experiments. A single value of D̅ and the first 10 Bessel roots (Scheme 1) were used to fit f vs t

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CONCLUSIONS Eighteen combinations of polycations and polyanions employed for PEC formation highlight the broad range of interaction strengths available. These energies or strengths are correlated somewhat with water content and the mobility of small ions within the PEC. Weak pairs of Pol+ and Pol− are more likely to be used for coacervates, to show “exponential” growth during multilayer formation,67,68 to exhibit labile F

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behavior during polyelectrolyte/polyelectrolyte exchange reactions,21 and to allow facile transport of small molecules or ions. Conversely, strong PECs are more likely to be glassy, nonlabile, and less permeable to small molecules or ions69 and will show linear growth in multilayer assembly. The listing and use of ΔG values in Table 2 simplify theoretical treatments of PECs. Rather than balancing multiple Coulombic interactions in an electrostatics approach, one can treat the interaction between Pol+ and Pol− as an ion pair competing with Pol+A− and Pol−M+ pairs using a single interaction energy and an equilibrium with the form of eq 2. Given the role of hydration in relative interaction energies, it would be most helpful to understand better the mechanism for hydration of polyelectrolyte repeat units and Pol+Pol− pairs and to define the locations of the water moleculesa job suited to molecular dynamics simulations.70

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.6b02445. Details on conditions for preparing complexes; TGA’s, scanning electron micrographs, undoping kinetics, and equilibrium doping curves for complexes; expansion of eq 4; diffusion fitting for PECs (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (J.B.S.). ORCID

Joseph B. Schlenoff: 0000-0001-5588-1253 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by grant DMR1506824 from the National Science Foundation.

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REFERENCES

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