When a polyanion (Pol -) and polycation (Pol + ) are mixed in solution, a polyelectrolyte complex or coacervate (PEC) may form which is an amorphous blend of the two polyelectrolytes. [1][2] The complexation event, a type of liquid-liquid phase separation, LLPS, can be represented as follows:
𝑃𝑜𝑙 -𝑀 + 𝑎𝑞 + 𝑃𝑜𝑙 + 𝐴 - 𝑎𝑞 → 𝑃𝑜𝑙 + 𝑃𝑜𝑙 - 𝑃𝐸𝐶 + 𝑀 + 𝑎𝑞 + 𝐴 - 𝑎𝑞 (1) where A -and M + are ions of salt MA. The entropic release of counterions is a major driving force for complexation. [3][4][5] Adding salt to the solution phase partially reverses Equation 1 in a process known as "doping." Doping breaks Pol + Pol -pairing interactions and additional water molecules usually accompanies doping. These effects reversibly plasticize the polymer Digby et al. Macromolecules 2022, 55, 3, 978-988 doi.org/10.1021/acs.macromol.1c02151 Accepted Version ("saloplasticity"), which softens the material and provides a spectrum of solid-like to liquid-like morphologies. 6 If sufficient salt is added to solution, Equation 1 may be fully reversed and the PEC may completely dissociate back into a single phase mixture. The point where this occurs is known as the critical salt concentration, CSC, or the "salt resistance," a term coined by Bungenberg de Jong in his extensive pioneering work on PECs. [7][8] The effect of salt concentration on the population of Pol + Pol -pairs may be interpreted using classical electrostatic screening arguments, [9][10] or by a more charge-specific competition between pairing of polyelectrolyte segments and (counter)ions. 11 The salt resistance is an important point on phase diagrams of PEC composition. 9 A sketch of a binary PEC phase diagram, showing salt and polymer concentrations, is given in Figure 1.
Typical phase diagram for liquid-liquid phase separation of PECs from oppositely-charged polyelectrolytes. The PEC phase is rich in polymer whereas the dilute phase contains little, or no, polymer. The critical salt concentration or salt resistance is shown by the point "CSC." Tie lines (red dotted) are for conditions where the enthalpy of complexation, ΔHPEC, is positive (> 0), negative (< 0) or = 0 (isothermal). If ΔHPEC is > 0 the salt concentration is greater in the PEC phase and vice versa if ΔHPEC is < 0. 12 For ΔHPEC = 0 the PEC and dilute phase salt concentrations are equal. In cases where the CSC is not obtained, the top portion of the phase diagram will instead appear to follow the black dotted lines, not showing an apex. With sufficient added salt polyelectrolytes may become insoluble.
The salt resistance is commonly used as a measure of the interaction strength of the Pol + Pol -pairs within a PEC. The CSC, which varies strongly with the identities of Pol + and Pol -and also on the nature of MA, is at (for ΔHPEC = 0) or near the maximum in the binodal, as shown in Figure 1. The "tie lines," examples shown in Figure 1, connecting the binodals, or boundary between PEC and dilute phase, are also of interest. 13 Negative tie lines indicate a lower concentration of salt in the PEC, [MA]PEC, than in the dilute phase, [MA]s; positive tie lines the reverse; and level tie lines mean [MA]PEC = [MA]s. 14 The free energy of PEC formation/phase separation, ΔGPEC is given by ΔHPEC -TΔSPEC. ΔSPEC is always positive at low salt concentrations. The ΔH term reports the sum of all specific interactions: electrostatic, hydration, hydrophobic, hydrogen bonding, and dipolar. Calorimetry studies of polyelectrolyte complexation rarely reveal an athermal process, 3-4, 12, 15-21 although this condition is almost met by a system comprising poly(diallyldimethylammonium), PDADMA, and poly(styrene sulfonate), PSS in KBr. 6 It has been demonstrated previously that when the enthalpy of complexation between two polyelectrolytes is endothermic, a polyelectrolyte multilayer made with those two polymers is likely to grow exponentially. 4 When interactions are coupled to charges, the ion distribution between the solution phase and PEC phase follows a Donnan equilibrium modified by the complexation enthalpy. [11][12] The Donnan equilibrium, describing the distribution of small ionic species across a semipermeable membrane that has macroions restricted to one phase, 22 accurately predicts the distribution of several ionic species. 12 Though the CSC has been accepted as a general phenomenon for PECs, there are some instances where it has not, or cannot, be observed. A survey of the literature indicates that PECs using polycarboxylates as Pol -show a CSC at relatively low salt concentration, whereas a higher, or unattainably high, concentration of salt is needed to completely separate PSS from polycations. Curiously, for the same PDADMA/PSS PEC, a minor switch from NaCl to KBr makes the difference between achieving a measurable CSC or not. 23 The difference is: with Cl -ΔHPEC is exothermic while with Br - ΔHPEC ≈ 0. 12 In a site-specific model it is theorized that when complexation is endothermic, the salt ions have a preference to act as counterions for charged repeat units within the PEC, breaking Pol + Pol -pairs. Conversely when complexation is exothermic, the salt ions prefer to act as co-ions and not break pairs. 11 PEC stability against added salt is further complicated if at least one of the polyelectrolytes is a weak polyacid/base (i.e. has a pH dependent degree of ionization). 17,[24][25] Weak polyelectrolytes such as polyacrylic acid, PAA, have been extensively used to prepare PECs and thin films of polyelectrolyte complex made by the "multilayer" method. The opportunity to vary the solution charge density while constructing multilayers was exploited by Rubner and coworkers 24,26 and others, 17 who observed pKa shifts on complexation and suggested potential applications. [27][28] . Usually, bulk PECs from weak polyelectrolytes have been investigated under conditions where the polyelectrolyte is nearly fully ionized. [29][30] The term "coacervate" was used to describe the polymer-dense phase for LLPS of biopolymers. 9 Bungenberg de Jong's earliest work on coacervates 8 recognized the potential importance of LLPS (by charge pairing of oppositely-charged biopolymers) in the formation of biologically relevant structures. Oparin carried on this idea (and the term) in his postulates on the origin of life. 31 Charge pairing in biomolecules occurs between pH dependent units (carboxylate, amine, phosphate, imidazole). Shifts in pKa of peptide residues due to changes in environment, including the proximity of oppositely charged groups, in folded proteins have been extensively investigated by biochemists. 32 Only histidine and cysteine residues have pKa values around 7, suggesting at physiological pH they would be the only catalytically active amino acids. 33 However, it has been shown that folded protein environments can shift the pKas of nearly all ionizable groups close to physiological pH. 34 The pKa shift of these groups can be extreme, for example certain lysine residues have been shown to shift by 4.7 pH units. 35 The purpose of the present work is twofold: first, potential limitations of defining PEC stability by the salt resistance are highlighted. Second, the essential contribution of ionization enthalpies of weak polyelectrolytes to PEC salt resistance measurements is quantitatively explored. When PAA is complexed with PDADMA, the degree of PAA ionization within the PEC is always greater than the degree of ionization of
Materials. Poly(diallyldimethylammonium chloride) (PDADMAC, molar mass 200,000-350,000 g mol -1 ) and poly(4-styrenesulfonic acid, sodium salt) (PSSNa, molar mass 75,000 g mol -1 ) were from Sigma-Aldrich. Prior to use both polyelectrolytes were dialyzed (3,500 molecular weight cutoff tubing, SnakeSkin TM , ThermoFisher) against deionized water for 48 h, with water replacement every 12 h. Polyelectrolyte solutions were then freeze-dried (Labcono, FreeZone 105). Poly(acrylic acid) (PAA, molar mass 250,000 g mol -1 ) was from Polysciences, Inc. and used without further purification. Sodium chloride and sodium bromide were supplied by Sigma-Aldrich and dried at 110 o C for 24 h. Hydrochloric acid (VWR Chemicals BDH, 1.0 N) and sodium hydroxide standard (Hach, 1.00 N) were used as received. 2-(N-morpholino)ethanesulfonic acid (MES), 3-morpholinopropane-1-sulfonic acid (MOPS), N-[tris(hydroxymethyl)methyl]-3-aminopropanesulfonic acid (TAPS), N-cyclohexyl-2-aminoethanesulfonic acid (CHES), and N-cyclohexyl-3-aminopropanesulfonic acid (CAPS) were from Sigma-Aldrich and used as received. All solutions were prepared using deionized water (18 M cm Barnstead, Nanopure).
Isothermal Calorimetry, ITC. ITC was performed using a VP-ITC (MicroCal Inc.) calorimeter. The ITC was calibrated with an internal y-axis calibration followed by a standard titration between hydrochloric acid and Tris base. Prior to loading, both syringe and sample cell solutions were matched in pH using dilute NaOH or HCl. All samples were degassed for 10 min at room temp. Approximately 300 µL of a 10 mM polycation in 0.05 M NaCl was loaded into the syringe. 10 µL of the syringe solution was manually discharged from the syringe to relieve any back pressure from the loading proccess. Prior to filling, the sample cell (1.4138 mL) was washed with 0.5 mM polyanion in 0.05 M NaCl. The syringe was rotated at 260 rpm in the sample cell with an injection size of 4 µL per aliquot at a rate of 0.50 µL s -1 , with 240 s between injections. The heat flow was recorded as a function of time at 25.0 °C for all samples. Enthalpies were calculated by summing the total heat generated to the 1:1 end point with a correction for the background dilution enthalpy. Acidic conditions below pH 4 could not be probed without risk of damage to the instrument.
pH Titrations of PAA. The potentiometric titration was performed with a glass pH/ reference electrode, calibrated with buffer solutions of pH 4.00, 7.00, and 10.00. The titration was performed from the alkaline region, starting from a solution of 0.01 M PAA, 0.02 M NaOH and varying NaCl concentration. To these solutions, 0.100 M standard HCl solution was added with a micropipet at room temperature. The initial volume of the polymer solution was 15 mL. PEC Tablets. PECs of PDADMA/PAA and PDADMA/PSS were complexed using equivolume amounts of 0.125 M polyelectrolyte in 0.25 M NaCl. The resulting PECs were allowed to stir for 24 h at room temp, followed by a water wash every 12 h for 72 h, to remove ions. The PECs were stirred until the conductivity of the water solution was less than 10 µS cm -1 . PECs were then dried for 24 h at 110 °C and ground into a fine powder. The powders were placed into an 8 mm diameter stainless steel mold with a drop of water. A stainless steel weight of appoximately 8 kg was placed onto the mold and the PEC pressed into a circular tablet over 24 h under pressure. These tablets were used for ATR-FTIR and radiolabeling experiments. ATR-FTIR. ATR-FTIR specta were collected using a ThermoScientific Nicolet iS20 with a Pike MIRacle universal ATR attachment fitted with a single reflection Digby et al. Macromolecules 2022, 55, 3, 978-988 doi.org/10.1021/acs.macromol.1c02151 Accepted Version diamond/ZnSe crystal and high pressure clamp. A stainless steel well was machined to fit onto the crystal plate to allow solid samples immersed in solution to be pressed onto the crystal while preventing evaporation of water from the samples. All PEC spectra were taken with the PEC tablet immersed in either 0.05 M or 0.30 M NaCl at each specified pH. The pH listed was recorded after 24 h of immersion in the specified salt concentration. Background for all spectra was ambient air, and a spectrum of 0.05 M or 0.30 M NaCl was subtracted from all spectra. To find α2, the degree of PAA ionization in PDADMA/PAA PEC, PDADMA/PAA tablets were placed into the reservoir filled with a solution of known pH and pressed onto the ATR crystal with a highpressure clamp. Pressing the tablets while they were immersed in the solutions ensured that they remained fully hydrated. Two experimental challenges limited the extremes of pH. First, PEC tablets at lower pH expanded and became more fragile, which occasionally resulted in splitting of the PEC when pressed with the clamp. At high pH tablets became viscous and liquid-like while not swelling as much.
UV-Vis. UV-Vis experiments were conducted on a Cary 100 Bio UV-Vis spectrometer to determine the CSC of PECs. PDADMA/PAA PECs were dissolved in a 4 M NaCl at pH 12, resulting in a final PEC concentration of 0.1 M. A portion of the resulting solution was placed in a quartz cuvette with a reference solution of equal NaCl concentration and small aliquots of 1.0 M HCl were added to both cuvettes until an increase in scattering was observed at 390 nm and the pH was then recorded. Other cuvettes were pH adjusted from 5 -12 and water was added to dilute the NaCl concentration until an increase in scattering was observed at 390 nm and the pH was then recorded. Similar experiments were conducted using PDADMA/PSS in NaBr and NaCl, however the resulting PEC in NaCl formed a solid that stuck to the sides of the cuvette. Dynamic Light Scattering, DLS. PDADMA/PAA aggregate sizes at low pH were determined by dynamic light scattering using a goniometer system (ALV CGS-3-A0-111, Langen, Germany) equipped with a He-Ne laser (λ = 632.8 nm, 22 mW) and vertically polarized light. At an angle of 30°, measurements were taken in 10 mm capped cylindrical borosilicate glass tubes through a reservoir filled with a refractive index matching liquid (toluene). The polymer samples of 12.5 mM concentration at pH 1.15 were prepared by diluting a stock solution of dissolved PEC in 4.0 NaCl, with a pH adjustment with 1.0 M HCl. By pseudo-cross-correlation of the signals from two photomultipliers, the intensity autocorrelation function g(2)(q,τ) where q = 4πnD sin(θ/2)/λ was obtained with suppressed noise by using ALV correlator software V.3.0. The hydrodynamic radius Rh was calculated along with the distribution of Rh.
A radiolabeling technique was used to determine the stoichiometry of as-prepared PEC tablets. Radiolabeled ions label the extrinsic or counterioncompensated sites of undoped PECs with high precision and sensitivity. Thus, 22 Na labeled NaCl "hot" stock solution was prepared by adding 1 mL water into 100 μCi 22 NaCl (γ-emitter, half-life 950 days, Emax = 511 keV, PerkinElmer), whereas 35 S labeled Na2SO4 "hot" stock solution was prepared by adding 1 mL water into 1 mCi Na2 35 SO4 (β-emitter, half-life 87.4 days, Emax = 167 keV, PerkinElmer). 5 mL 0.1 M NaCl hot solution was prepared by adding 0.25 mL NaCl hot stock solution (25 μCi) into 4.75 mL water mixed with 0.0292 g NaCl (0.0005 mol), which gave a specific activity of 0.05 Ci mol -1 . Similarly, 5 mL 0.1 M Na2SO4 hot solution was prepared by adding 0.05 mL Na2SO4 hot stock solution (0.05 mCi) into 4.95 mL water mixed with 0.071 g Na2SO4 (0.0005 mol), which gave a specific activity of 0.1 Ci mol -1 . A 10 -5 M NaCl or Na2SO4 rinse solution was prepared by adding 10 μL of the 0.1 M hot solution to 100 mL water. To determine the amount of excess polyanion, PEC tablets were first immersed in 10 mL non-labeled 0.1 M NaCl solution for 24 h to allow complete ion exchange. After that, each PEC tablet was immersed in 5 mL 0.1 M NaCl hot solution for 24 h to allow radiotracers to label the PSS extrinsic sites. Then the radiolabeled PEC tablet was rinsed with 2 batches of 5 mL NaCl hot rinse solution for 24 h each ( 48Digby et al. Macromolecules 2022, 55, 3, 978-988 doi.org/10.1021/acs.macromol.1c02151 Accepted Version h total) to remove any residual isotopes that were not involved in radiolabeling of extrinsic sites (for example, in pores). The rinsed PEC tablet was then immersed in 5 mL non-labeled 0.1 M NaCl solution for 24 h to extract 22 Na + associated with the extrinsic sites. Finally, a mixture of 500 μL extracted solution and 5 mL liquid scintillation cocktail (LSC, MP Biomedicals) was prepared in a 20 mL plastic vial. Once the mixture turned transparent, this vial was mounted on top of an RCA 8850 photomultiplier tube in a dark box and counted for at least 15 min. A calibration curve was obtained by adding known amounts of hot solution into 5 mL LSC to convert counts per second, cps, to moles of extrinsic sites. The same radiolabeling procedure was repeated with Na2 35 SO4 hot solution to determine the amount of excess polycation. Finally, PEC tablets were collected and rinsed in water for 24 h, dried at 120 °C in a vacuum oven for 24 h, and weighed to obtain total polymer dry weight. The total counts ranged between 54000 and 720000 with respective counting errors of 0.4 and 0.1%.
Figure 1 shows a typical salt resistance measurement for a PEC made from a strongly-dissociated (i.e. pH-independent) pair of polyelectrolytes. In this case, PSS and PDADMA have been complexed from dilute solution, yielding a cloudy suspension of particles rather than a mass that settles to the bottom of the container (which is produced from concentrated polyelectrolyte solutions). The suspension scatters light and is detected via turbidimetry using a wavelength of light that is longer than any of the specific UV-vis absorption features (i.e. peaks from electronic transitions) from either polymer. In this classical method, as salt is added the solution becomes clear at the CSC. 7,36 Dynamic light scattering is also a sensitive method for detecting complete dissolution of solid PEC.
Two closely-related sodium salts, NaBr and NaCl, have been used in an attempt to reach the CSC for the PDADMA/PSS complex. Figure 1 shows that CSCNaBr is at 2.6 M NaBr, but CSCNaCl cannot be achieved up to 3.4 M NaCl. A similar result was seen by Ali and Prabhu comparing KBr and NaCl for PDADMA/PSS. 23 The CSC is often explained using the continuum electrostatics arguments of salt "screening," where higher ionic strengths weaken the electric fields between charges. Classical screening arguments are unable to account for the substantial difference in PEC response to NaBr versus NaCl seen in Figure 2. Scheme 1 illustrate a final dilemma: the more salt that takes Path 1 the more volume is created within the PEC that can be occupied as co-ions and the more f decreases as the [salt] nears the CSC, rapidly inflating the PEC with water and salt as it does so. 6 Thus, although Path 4 is anticipated to reach the CSC, Path 5 becomes more favored.
The preferred path may be understood using ΔHPEC as a measure of the "preference" of an ion to locate next to a polymer repeat unit as a counterion rather than exist as a PEC co-ion, which is assumed to be in a (hydration) environment similar to that of the bulk solution. When the source of ΔHPEC is attributed to ion specificity, exothermic ΔHPEC (complexation is in the opposite direction to that shown in Scheme 1) indicates the ion prefers a co-ion environment whereas an endothermic ΔHPEC shows the ion prefers to be a counterion. Because ions enter a stoichiometric PEC in pairs (to maintain charge neutrality) the preferences of both ions are convoluted, but a series of anions showed a systematic trend of ΔHPEC along a Hofmeister series. 12 Raman spectroscopy studies of PDADMA bearing counterions along this series showed excellent correlation with a change in water network hydrogen bonding, 3 emphasizing the specificity of the hydration environment for different ions.
The near-CSC scenarios of Paths 4 versus 5 may now be used to understand the strong differences between similar salts seen in Figure 2. Complexation in Br -is nearly athermal (about +200 J) and about 2.4 kJ more endothermic than in Cl -(ΔHPEC ≈ -2.2 kJ) 12 implying Cl -prefers the co-ion environment more than Br -does. As the PEC becomes more doped with NaCl, f remains low, allowing the PEC to retain Pol + Pol - pairs (Path 5). At sufficiently high concentration the salt may even dehydrate the PEC via osmotic pressure, making it impossible to dissolve. 37 Even -2.4 kJ mol -1 (about 1 kT) of ΔHPEC is enough to suppress the observation of the CSC. 12,23 Thus, salt resistance and the top part of the phase diagram (Figure 1) may not be measurable or achievable and will depend strongly on the nature of MA. Values of f computed by Ghasemi et al. 38 decreased substantially with salt addition to PDADMA/PSS, leading to inflation of the PEC near the CSC.
The ease of breaking pairs along Path 1, crucial to dissolving PECs with salt, is described by an unpairing equilibrium constant, Kunpair
using concentration in place of activities (i.e. assuming activity coefficients = 1 or, more likely, they cancel). Greater values of Kunpair means weaker complexes. As a measure of stability against added salt, Kunpair may be preferred to the CSC because the composition is not changing as drastically with [salt] at low [salt] as it is near the CSC. On the other hand, salt doping measurements are more time-consuming than simply increasing [salt] until the complex dissolves. The PEC in Figure 2 between aromatic sulfonate and quaternary ammonium happens to be of "medium" strength in the combinations of different polyanions and polycations. 39 Polycarboxylates form weaker complexes that are more likely to be liquid-like. 39 For this reason, early work on PECs, which focused on bio-, or bio-derived, polyelectrolytes of low charge density, tended to report fluid-like coacervates with an emphasis on spontaneous droplet formation, compartmentalization, and possible connections with origin of life. [7][8]31 Recent works have focused on potential applications of pH dependent complexes such as drug delivery systems 40 or self-healing materials. 41 PDADMA/PAA has a lower salt resistance 39 (see Supporting Information Figure S1) than that of PDADMA/PSS. When PAA is fully ionized, the complexation turns out to be endothermic (about +2 kJ mol -1 , vide infra), reinforcing Paths
The stability of PECs with pH-insensitive charge is indifferent to the solution pH (except for additional doping induced by added ionic strength at extremes of pH). Likewise, ΔHPEC does not depend on pH. As an example, ΔHPEC for PDADMA/PSS formation is about -2.2 kJ mol -1 over the pH range 6 to 10 (see Supporting Information Figure S2).
Unlike PDADMA/PSS, the CSC for PDADMA/PAA shows a distinct pHdependent response (Figure 3). Above about pH 7 the CSC is found at about 0.5 M NaCl. At lower pH, the CSC rises sharply and exceeds experimentally accessible [NaCl], limited by the solubility of PAA. It was surprising to discover clear solutions could not be obtained at pH < 2 for any [NaCl]. Under sufficiently acidic conditions, no charges should reside on PAA and complexation should thus be intuitively "turned off." In fact, though solutions were less scattering at low pH, polyelectrolyte association was still observed for nominally neutral PAA, indicated by milky solutions. DLS showed particles with hydrodynamic radius, Rh, of about 1 μm and rather narrow size distribution (see Supporting Information Figures S3 andS4). Previous literature has suggested that when PAA has little to no charge, it can still bind to other molecules via hydrogen bonding [42][43] and/or hydrophobic interactions not coupled to ions. From Figure 3, whichever interaction may dominate is not sensitive to [salt]. Complexation of neutral species via dehydration has been termed "water-mediated complex coacervation." 44 Both Alonso et al. 17 and Vitorazi et al. 18 18 Using Good's buffers, which are known to not interact significantly with bio based polymers, the PDADMA/PSS complexation enthalpy was reduced presumably due to doping (see Supporting Information Figure S2). In addition, the enthalpy of buffer ionization contributes to the measured ΔHPEC. Therefore, calorimetric measurements in this work focused on titrations of PDADMAC into PAA at low salt concentrations in solutions carefully pH-adjusted using HCl or NaOH but using no buffer. During complexation, pH sensitive polyelectrolytes are known to undergo pKapp shifts. 24-25, 28, 45 This forced ionization of functional groups is also known to be induced by oppositely-charged amino acids in proteins and is considered central to the catalytic ability of enzymes. 35,46 Scheme 2 summarizes the way complexation-induced shifts in ionization occur. The example shown is for a negative weak acid polyelectrolyte, Pol -Na + when completely ionized and PolH when fully protonated, with solution degree of ionization α1. Complexation with pH-independent strong polyelectrolyte Pol + A -results in a PEC wherein the degree of ionization of Pol -is α2. ΔHPEC therefore includes a component αΔHi where ΔHi is the enthalpy of ionization, represented by where α = α2 -α1
Equation 3 shows ΔHPEC is determined by the sign and magnitudes of ΔHPair, ΔHi, α1 and α2. At high pH, α2 → 1 and α → 0 so ΔHPEC → ΔHPair. From Figure 5 ΔHPair was estimated to be 2320 J mol -1 . Scheme 2 does not include doping by salt, which effectively removes Pol + Pol - from the cycle shown. If salt doping were included in Scheme 2, then the equations would be modified by a factor of y, where y is the fraction of Pol + Pol -converted to Pol + A -+ Pol -M + in the PEC phase. Scheme S1 in Supporting Information presents this more complex situation. The main point is that salt doping reduces the magnitude of ΔHPEC but does not change the sign.
The α1 values for synthetic polyacids such as PAA as a function of pH were investigated by Kern, 47 and later by Katchalsky and Spitnik, 48 who found that a simple Henderson-Hasselbalch, H-H, equation did not fit the broad titration curves observed. A rearranged form of Katchalsky's extended H-H equation for a fixed [NaCl] is 25,49
Where pKapp is the apparent pKa (pH for 50% neutralization) and n is an interaction parameter between neighboring ionized groups on the polyelectrolyte. 49 In certain cases it also may be related to a conformational change in the polyelectrolyte, [49][50] but not for PAA. 49,51 This interaction parameter, independent of molecular weight 52 and polyelectrolyte concentration, 48 depends on the salt concentration of the surrounding solution. 48 Extended H-H plots for PAA at different [NaCl] are given in Figure S6. The pKapp and n values are summarized in Table 1. 1 shows that as the salt concentration increases there is a decrease the pKapp and n. Few previous works have looked at more than five concentrations of NaCl with PAA: some of the most comprehensive are those of Kodama et al. 53 and Dickhaus et al. 54 The pKapp of 5.41 for 0.5 M NaCl is nearly identical to the value of 5.4 reported by Petrov et al. 25 and the pKapp value of 5.17 for 1.0 M NaCl is close to the value of 5.2 reported by Kim et al. 49 The values reported by Dickhaus et al. at identical polyelectrolyte and salt concentrations appear to be approximately half a pKa unit lower than those shown in Table 1. 54 Figure 6 displays both the experimental α1 points along with a solid line representing the fitted α1 at any pH. Good agreement is shown throughout the fit except for extremes of the experimental titration curve.
According to Kodama, for PAA in solutions of NaCl, where pK0 is the monomer pKa and log[Na + ]p is the Na + concentration inside the polymer coil. 53 So adding more solution NaCl shifts the solution pKapp lower. Similarly, the ionization of Pol -in the PEC reads as follows
so more NaCl shifts the PEC pKapp higher. At sufficiently high [NaCl] pKapp,PEC → pKapp,solution → pKa,monomer (i.e. acetic acid pKa = 4.75). The maximum salt concentration is limited by the fact that 1.5 M NaCl is near the Θ condition for PAA. 55 1. Diamond shaped points are for the neutralization of PAA, degree of ionization α2, within PDADAMA/PAA PEC. ΔpKa is the shift in pKapp between PAA in solution and within PEC. The difference in degree of ionization of PAA in solution and within PEC is Δα, which depends on arrow shows the pKa of acetic acid. Note that adding salt moves pKapp in solution lower, towards pK0, while pKapp in the PEC increases.
To solve for Δα and ultimately ΔHi in Equation 3, α2 is needed. Various methods of measuring the ionization inside a PEC have been used. Petrov et al., using potentiometric titrations, found that α2 and pKapp values were identical in both bulk PECs of PDADMA/PAA and in multilayer shells. 25 They reported pKapp values of 3.6 and 4.0 in water and 0.5 M NaCl, respectively, and pKapp shifts (ΔpKa) of 2.85 and 1.4 respectively. Using computational models, Salehi and Larson 56 employed a system of specific charge-charge interactions connected by equilibria including those shown in Scheme 2 and were able to model the bulk titration curve reported by Petrov et al. for PDADMA/PAA. 25 Burke and Barrett using zeta potential measurements of colloidal particles coated with multilayers, reported PAA pKapp shifts of almost 4 units in PAH/PAA. 57 Using FTIR, Choi and Rubner demonstrated pKapp values of PAA in PEC multilayers of 2.2 with PAH and 3 with PDADMAC. 24 FTIR of a multilayer film of linear poly(ethylene imine) and PAA, reported a pKapp of PAA between 2.3 and 2.5. 58 The internal state of ionization within PDADMA/PAA PECs as a function of solution pH was determined here using ATR-FTIR. To obtain reference spectra of PDADMAC, fully ionized (α1 = 1) PAA and fully protonated (α1 = 0) PAA, concentrated solutions of PDADMAC, and PAA at high (pH 13) and low (pH 2.5) were drop cast directly on a single reflection diamond ATR crystal. Figure 7 shows two distinct peaks associated with the carboxylic acid group of PAA. The C=O bond stretching in neutral PAA, PAAH, at pH 2.5 appears at 1700 cm -1 while at pH 13 the asymmetric stretching band of the ionized carboxylate appears from 1610-1500 cm -1 .
Figure 7. ATR-FTIR spectra of PAA dried from high (pH 13) and low pH (pH 2.5) PAA solutions; and PDADMAC at 25°C. α2 was calculated by Equation 7, using a ratio of the protonated carboxylic acid C=O stretching to the PDADMA peak at 1475 cm -1 , with half peak integrations from 1760-1705 and 1495-1470 cm -1 , respectively. Judging from the titration curve of PDADMA/PAA reported by Petrov et al., it was assumed that for the PEC in 0.05 M NaCl at pH 9.59 PAA is fully ionized and at pH 1.75 PAA is fully protonated. 25 ATR-FTIR spectra of PDADMA/PAA in 0.05 M NaCl can be found in Figure 8, while the spectra of this PEC in 0.3 M NaCl are given in Figure S7 with α2 in Supporting Information Tables S1 andS2. Tablets immersed in 0.05 M NaCl and 0.30 M NaCl have pKapp values of 2.69 and 3.77 compared with solution pKapp values of 6.08 and 5.62, respectively. The respective pKa shifts of 3.39 and 1.85 units fall within expectations based on the literature and display nearly identical curve shapes. [24][25] Figure 6 includes both α1 and α2 titration curves for comparison. With the titration curve for PDADMA/PAA in 0.05 M NaCl giving α2, ΔHPEC in 0.05 M NaCl can now be calculated. ΔHPEC calculated from Eq 3 using an averaged ΔHi = -2.84 kJ mol -1
Though Equation 4 predicts α1 at pH 10 is 0.99, literature reports suggest that α1 is 1 at this pH [24][25] thus Δα is 0. A HPEC value of 2.32 kJ mol -1 , estimated from Figure 5, was used along with the values in Table 2 to calculate ΔHi, which was found to average -2.84 kJ/mol.
ΔHPair and ΔHi are almost equal and opposite. Equation 3shows that these work against each other to lower HPEC as pH decreases. Because α2 is near unity for all pH > 4, only when Δα is maximized can ΔHi switch HPEC to exothermic. It is surprising that such a small degree of exothermicity can prevent dissolution, but it suggests the ability to observe a CSC depends sensitively on whether HPEC is exothermic or endothermic.
Nonstoichiometry within PECs has a significant influence on mechanical properties such as the modulus and glass transition temperature. 59 It is not known how the pKapp shifts in response to nonstoichiometry. In the current work, only (nearly) stoichiometric PECs of PDADMA/PSS and PDADMA/PAA were prepared and validated using radiolabeling techniques with errors as low as 0.1% (Figures S8 andS9, Table S3). For the PDADMA/PAA tablets used to determine the CSC and α2, the stoichiometry was 1.026:1 (i.e. 2.6 % excess PDADMA). PDADMA was complexed with PAANa at pH >7, which corresponds to full ionization within the PEC (Figure 6).
The CSC represents a convenient comparison for the relative "strengths" of coacervation/complexation of synthetic and bio polyelectrolytes. If the pairing macromolecules bear the same combination of charges (e.g. always lysine and glutamic acid), and NaCl near pH 7 is used, the CSC may provide a reliable comparison. The contribution of an endothermic HPEC to enforcing Path 1→3→4 in Scheme 2 should be appreciated.
There is more diversity of charged functional groups available for synthetic polyelectrolytes. Aromatic sulfonate, i.e. PSS, has been a staple of all aspects of research into synthetic polyelectrolytes, but is not one of the typical charges in biopolymers (although the aliphatic sulfate group is found, for example on heparin). Studies of PECs in non-biological systems also offer greater flexibility in choice of pH and salt environment. There are some caveats: individual polyelectrolytes must be soluble in the salts used to break up PECs. For example, hydrophobic anions associate more strongly with Pol + , giving more endothermic HPEC values. An example is PDADMA in SCN -, I -, and ClO4 -, ions at the hydrophobic end of the Hofmeister series. 12 Though these ions dope a PDADMA/PSS PEC strongly, PDADMA is not soluble in a solution of the ions and no CSC may be observed.
The stability of PECs against salt depends on the volume (not linear) charge density. 12 A PEC relies on accommodating salt ions in response to increasing solution Digby et al. Macromolecules 2022, 55, 3, 978-988 doi.org/10.1021/acs.macromol.1c02151 Accepted Version ionic strength. PECs with higher charge density are able to accomplish this to higher ionic strength without breaking apart. 12 Researchers are often interested in "tuning the (linear) charge density" of a polyelectrolyte, which makes weak acid/bases and control of pH an obvious experimental variable. As shown above, the linear charge density, in terms of α, of PAA in PEC is close to 1 for most pH values. What is actually being "tuned" is the shift in ionization, Δα, which is a driving force for complexation (see column 6 Table 2).
The salt resistance, given by the critical salt concentration, is a key feature in the phase space of coacervates made from charged bio(polymers). It is not always observed for reasons that are uniquely polymeric. Phase separation is preceded by gradual unpairing of charge pairs with added salt, but the fraction f of salt ions actually breaking Pol + Pol -pairs decreases towards the CSC.
The CSC is promoted by endothermic pairing or complexation of Pol + and Pol -, which is an indication of ion specificity (or preference for counterion versus co-ion roles). Estimating the value of f as a function of ion content is a challenging but required step for modeling PEC response to salt: f depends on how much volume is created by breaking a charge pair -the more volume the lower f. Judging from the comparison of HPEC and the CSC in Figure 5 there may be a fine line between soluble and insoluble PECs. It may require less than 1 kJ of HPEC to make the difference between solubility and insolubility. This may have significant consequences in disease conditions characterized by the aggregation of biopolymers. 60 For example, a change in amino acid or post-translational modification could mean the difference between a reversibly-associating pair of proteins or folding and an irreversibly-aggregated system.
When weak polyelectrolytes are complexed their degree of ionization changes. It has been demonstrated that enthalpies due to changes of ionization are important contributors to ΔHpec and to the phase space of PECs. Because PEC pairing enthalpies are usually small, even slight changes in ionization are significant. Whereas polycarboxylates experience lower pKapp on complexation, the pKapp of polyamines increases when they complex. 57 Thus, complexation promotes the ionized form of both polycarboxylates and polyamines. For the present example, ionization is exothermic, which works against achieving full unpairing of PECs. The maximum measurable change in ionization occurs at around pH = 4, below which PDADMA/PAA cannot be fully dissolved. Shifts in pKapp when PAA is incorporated into the PEC studied here are as large as 3.6 pH units. The mechanisms and magnitudes of this pKapp shift have much in common with those induced in amino acids within folded proteins, where such pKapp shifts are thought to be essential in enzyme activity. While naturally-occurring coacervates, such as those formed into membrane-less organelles in cells, may not have the sophisticated structure of folded proteins, pKapp shifts essential to accelerating reactions may still be realized by proximity to oppositely-charged repeat units close enough to form charge pairs as seen here. Catalysis need not require structure.
For the PEC investigated here, both the enthalpy of ionization and the entropy of complexation are coupled to the ions. If the driving force for coacervates includes interactions that are relatively insensitive to ionic strength, such as hydrogen bonding, 43 the CSC may not be achievable, or at least measurable. Hydrogen bonding between polymers can be challenged by small or macro-molecules with hydrogen bonding properties, or by increasing the temperature.