Proton Dissociation of Sulfonated Polysulfones: Influence of Molecular

Feb 5, 2015 - The basic measuring principle is known for more than 40 years, and measurements were carried out on electrolytes containing simple ionic...
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Proton Dissociation of Sulfonated Polysulfones: Influence of Molecular Structure and Conformation Andreas Wohlfarth,*,† Jens Smiatek,‡ Klaus-Dieter Kreuer,*,† Shogo Takamuku,§ Patric Jannasch,∥ and Joachim Maier† †

Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, Germany Institute for Computational Physics, University of Stuttgart, Allmandring 3, 70569 Stuttgart, Germany § Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany ∥ Department of Chemistry, Lund University, 22100 Lund, Sweden ‡

S Supporting Information *

ABSTRACT: The counterion condensation behavior of proton conducting sulfonated polysulfones has been investigated by combining electrophoretic NMR, pulsed magnetic field gradient NMR, and conductivity measurements on monomeric and polymeric samples with concentrations of ionic groups in the range where dissociation is not complete (IEC = 4.55−7.04 mequiv g−1). In this regime, counterion condensation is shown to critically depend on details of the molecular structure, and all atom molecular dynamics (MD) simulations reveal the formation of well-defined ionic aggregates (e.g., triple ions). The corresponding global minima of the free energy are suggested to be the result of a delicate balance of the energetics involved in conformational changes, formation of ionic aggregates, and solvation. This goes beyond Manning’s counterion condensation theory and has important implications for the development of membranes with high ionic conductivity as needed for many electrochemical applications such as fuel cells and batteries.

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INTRODUCTION In the quest for higher ionic conductivity of polymeric electrolytes for electrochemical applications, increasing the density of ionic groups is one of the promising strategies. In the case of solvated ionomers, this may lead to the point where the system may rather be considered to be a polyelectrolyte characterized by the appearance of so-called polyelectrolyte effects. Among others, they comprise reduced ion dissociation which is commonly described within the framework of Manning’s counterion condensation theory.1 Here, the electrostatic screening effect of the solvent is approximated within the Debye−Hückel limit for a linear arrangement of equidistant ionic charges. If the corresponding distance falls below the Bjerrum length, determined by the permittivity of the solvent, incomplete electrostatic screening predicts the occurrence of counterion condensation. Naturally Manning’s purely electrostatic considerations do not include influences of molecular conformations and short-range specific chemical interactions. It is therefore not surprising that quantitative information on the effective charge of macromolecules in solution, as obtained by a NMR technique designed by Scheler et al.,2 revealed deviations from the behavior as predicted by classical counterion condensation theory for various polyelectrolyte systems. When it comes to the design of separator materials for electrochemical energy conversion and storage devices, identification of those parameters controlling dissociation of highly acidic sulfonic functionalized systems (ionomers, polyelectrolytes) is, however, of paramount importance. Therefore, we have chosen to study the proton dissociation behavior of sulfonated poly(phenylene sulfones) in detail as © XXXX American Chemical Society

this polymer structure provides access to different local ion densities, polymerization degrees, and positioning of the sulfonic acid group (Scheme 1). The combined use of pulsed magnetic field gradient (PFG), electrophoretic NMR, and conductivity measurements reveals surprising new insights and together with the results of MD simulations provides rationales for explaining the importance of polymer conformation and specific ion solvent interactions for better understanding the observed dissociation equilibria (charge carrier formation). Finally, some implications for the design of separator materials for fuel cell and battery applications are discussed, and development strategies are specified.

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METHODOLOGY

Since the results from electrophoretic (E) NMR experiments are crucial for the key conclusion drawn in the present study, some critical issues of this technique are discussed here. The Nernst−Einstein equation (1) relates the electrical mobility μi and conductivity diffusion coefficient Dσi of a given charged mobile particle i: Dσi =

kBT μ ze i

(1)

Received: December 18, 2014 Revised: January 27, 2015

A

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Macromolecules Scheme 1. Chemical Structures of Investigated Materialsa

a From top to bottom: structure 1: 3,3′-disulfonate-4,4′-difluorodiphenylsulfone (SMSO2-207); structure 2: monosulfonated poly(phenylene sulfone) (sPSO2-220); structure 3: hypersulfonated poly(phenylene sulfone) (sPSO2-142), containing fully octasulfonated biphenyl units (two repeat units are shown for 2 and 3).

with e being the elementary charge, z the number of charges per particle, kB the Boltzmann constant, and T the absolute temperature. The conductivity diffusion coefficient Dσi actually equals the tracer diffusion coefficient Dtr as long as the elementary events leading to mobility in an electric field and diffusion show identical correlation which is particularly true in the case of vanishing correlation (random walk). Otherwise, the Haven ratio H, which is the ratio of the correlation factors for diffusion and mobility, relates Dσ and Dtr through Dtr = HDσ. In the present work, however, the diffusion and mobility of polyelectrolytes are recorded using very dilute solutions, for which correlation effects are negligible. Knowing the mobility (drift velocity in an electric field) and the tracer diffusion coefficient Dtr at a given temperature T, therefore, allows one to determine the number of charges per particle z directly through eq 1. z is an effective number of charges moving together with the particle. The number of charged species (ions) involved may actually be different since counterions are most likely in a continuum of states between the completely condensed (immobilized) and dissociated (mobile) state (two state approximation). In the present work, both Dtr and μ are determined through NMR techniques (PFG and E-NMR, respectively) using identical NMR signals. Complications stemming from different time, space averaging are therefore not an issue. For the applied techniques, the typical averaging time is of the order of milliseconds; i.e., the obtained number of charges per particle (here polyelectrolyte or monomer) represents the average on this time scale. Since the ion exchange rate of polyelectrolytes in solution is usually on a much shorter time scale, the numbers obtained in this work are expected to be very robust. It should be mentioned that the polyelectrolytes used had some polydispersity with corresponding spreads for Dtr and Dσ. We have therefore truncated small identical high diffusion/mobility contributions (∼12%) of the low molecular weight fractions for both PFG-NMR and ENMR experiments (see Figure S2a,b). In this way, the data could be fitted with single values for diffusion coefficient and mobility; in particular, averaging errors arising from nonlinearity of the diffusion (mobility)/molecular weight relationship are minimized.

Under the bottom line, we estimate an error of less than 10% for the number of charges per particle z (polyelectrolyte, monomer) obtained in this way. For determining the degree of dissociation, however, the number of ionic groups per particle zi has to be known as well, and the uncertainty of zi is virtually identical to this of the molecular weight (note that zi = Mn/EW, where EW is the equivalent weight). In the case of monomer 1, this is precisely known, but for the two polyelectrolytes 2 and 3, the errors in the determination of the molecular weight dominate the uncertainly of the degree of dissociation α = z/zi. At this stage, we can hardly comment on the error bars of Mn as obtained by gel permeation chromatography (GPC) (see also Table 1), but the fact that the values for α obtained in this way are in reasonable agreement with the values obtained by an independent method (compare the values shown in Tables 1 and 2) provides some confidence in the reliability of the applied methodology. In particular, the uncertainties in α do not seem to be critical for the semiquantitative conclusion drawn from the results of this study. It was Scheler et al. who first determined the effective charge of polyelectrolytes in solution by measuring their tracer diffusion coefficient DTr through PFG-NMR and their mobility μ through E-NMR.3 PFG-NMR is a well-established method for measuring reliably tracer diffusion coefficients;4 this does not apply for determining the mobility of charged species by ENMR. The basic measuring principle is known for more than 40 years, and measurements were carried out on electrolytes containing simple ionic species such as quaternary ammonium cations.5−7 However, it was the more recent methodological developments which enabled the application of E-NMR techniques to the characterization of more complex situations such as the electrophoretic water drag in ionomers,8 charged complexes,9 the electrophoretic mobility of large particles with multiple charges (biological macromolecules10 and colloid particles11), and most recently the mobility of complex ions in highly conducting ionic liquids.12 In the present case of dilute solutions of polyelectrolytes, a few characteristic features have to be considered. For this, we would like to recall that E-NMR is essentially a PFG-NMR experiment with an electric field present in the same direction as the magnetic field gradient. On top of the incoherent thermal motion of particles leading to attenuation (dephasing of the B

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Figure 1. (a) 1H NMR signal for different applied fields: left peak (polymer) with phase shift; right peak (residual H2O) without phase shift. (b) Linear trend of the phase angle as a function of the applied electric field of monosulfonated poly(phenylene sulfone) sPSO2-220 protonic form in D2O.

Figure 2. (a) Phase shift vs time of applied electric field. (b) Nyquist plot of aqueous PSSNa solution recorded in E-NMR cell showing the start of electrode polarization around υ = 25 Hz ≡ 40 ms.

electrode polarization; i.e., at frequencies ν > 25 Hz (corresponding to t = 40 ms) the current is ohmic through the bulk and capacitive in the electrode region, where charged species accumulate close to the solution/electrode interface. Only at low frequencies (ν < 25 Hz, t > 40 ms), the associated potential drop at the electrodes exceeds the point where electrolytic decomposition commences with the formation of gas bubbles inducing coherent displacements of the solution including both polyelectrolyte and water. In this regime, the phase of the polymer NMR signal broadens and the phase shift tends to level off (Figure 2a and Figure S2). For all measurements presented in this study, we have therefore limited the time that voltage is applied across the sample to the regime where ΔΦ is linearly dependent on time. Finally, it should be mentioned that the polymeric samples (2, 3) exhibited some polydispersity with the low molecular weight fraction naturally showing higher diffusion coefficients and drift velocities.15 This was immediately evidenced by the multiexponential echo attenuation recorded in PFG-NMR experiments (see Supporting Information Figure S2). Omitting data taken at low magnetic field gradients (G < 0.85 T m−1), however, leaves a single-exponential decay:

transversal magnetization) of the NMR signal observed in PFGNMR experiments, the coherent drift component of charged particles in the electric field leads to a phase shift which contains information about the displacement per time, i.e., the drift velocity of the charged particles (Figure 1).4 Under these experimental conditions, the NMR signal of uncharged diffusing species (e.g., solvent molecules) should show some dephasing, but no phase shift. However, this is only the case as long as the electric currents are not too high and the time the current is flowing does not exceed a certain limit. High currents may lead to convection (collective flow of neutral and charged species) as a consequence of internal heating which can be reduced by a complex cell design.12,13 The effects of time t, during which the voltage is applied and the current is flowing, we have investigated in pretests of the present study using the sodium form of sulfonated polystyrene (PSSNa) as dilute aqueous solution (see Supporting Information Figure S1). We have used a cell type described by Hallberg et al.14 with applied voltages up to U = 300 V well above the decomposition voltage of the aqueous sample. Nevertheless, a linear increase of the phase shift ΔΦ of the polyelectrolyte signals is observed for drift times up to t ∼ 40 ms, where ΔΦ tends to level off (Figure 2a). Interestingly, this limit corresponds to the onset of some irregular phase shift of the solvent signals clearly indicating emerging convection. As evidenced by the impedance spectrum (Figure 2b), this transition corresponds to the beginning of

ln(I /I0) = − γ 2δ 2g 2D(Δ − (δ /3))

(2)

with g being the integrated magnetic field gradient, Δ the time interval between pulses, δ their duration, γ the gyromagnetic C

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nm was generated by a PANalytical PW3830 X-ray generator operating at 40 kV and 50 mA. The samples were conditioned at 75% RH and placed in a solid sample holder and analyzed at 25 °C. Simulation Details. Classical atomistic MD simulations were used as to account for the effects arising from structural details down to the atomic level. Sophisticated parametrization approaches for all atoms of the polyelectrolytes ensure to reliably reproduce van der Waals and electrostatic interactions, which have a strong effect on the conformational behavior of the systems. Since the methodology does not allow for the cleavage of covalent bonds and does not account for proton solvation and polarization effects involved in hydrogen bond formation, systems have been simulated in their sodium (Na+) form only. In detail, we have modeled ortho and meta sulfonated dimers in sodium form with help of the PRODRG server20,21 and further evaluation with the ACPYPE script22 in combination with the ANTECHAMBER program23 for the evaluation of a GAFF-based force field.24 The partial charges were obtained by the usage of the AM1-BCC method25 to achieve a net charge of q = −2e. Two chlorine atoms one on each side of the dimer were added in the para position of the ring. To achieve electroneutrality, two sodium counterions were added to the system.26 The cubic simulation box for all systems had a length of 2.977 53 nm to yield a constant dimer concentration. The boxes were finally filled with TIP3P water molecules.27 The all-atom molecular dynamics simulations in an NVT ensemble were carried out by using the GROMACS 4.5.5 package28,29 with the Nosé−Hoover thermostat. The corresponding simulation parameters are identical to a previous study.30 We equilibrated the system for 500 ps, and the production run was conducted for 20 ns. The well-tempered Metadynamics simulations31 have been carried out for 10 ns with a biasing factor of 20. The initial height of the hills was 0.1 kJ mol−1, and we chose the distance between the sulfur atoms of the charged sulfonate groups as reaction coordinate. The width of the hills was 0.1 nm.

ratio, and I/I0 the areas of the signals with and without gradient pulses.4 Therefore, magnetic field gradients G > 0.85 T m−1 were chosen in order to eliminate contributions from low molecular weight fractions to both diffusion and drift velocity.

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EXPERIMENTAL SECTION

Materials. Disodium-3,3′-disulfonate-4,4′-difluorodiphenylsulfone (sMSO2-207) was purchased from Fumatech GmbH (Germany) and ion exchanged to its protonic form using Dow cation exchange resin Marathon C. Monosulfonated poly(phenylene sulfone) (sPSO2-220) was synthesized according to refs 16−18. Hypersulfonated poly(phenylene sulfone) (sPSO2-142) was synthesized according to ref 19. Acronyms are used for all materials according to their corresponding equivalent weight (EW, g equiv−1). All materials were dried in a vacuum oven at 120 °C and 10−5 bar pressure prior to use. Electrolyte solutions were prepared with double-distilled water. PFG NMR. PFG-NMR measurements were carried out on a Bruker 400 MHz Avance NMR spectrometer (9.4 T) equipped with a Bruker Diff60 diffusion probe head providing a gradient up to 30 T m−1 along the z-axis of the polarized field. A selective RF insert for 1H nuclei with NMR Larmor frequencies of 400.1 MHz was used. Polymer solutions were filled into standard 5 mm NMR tubes, and self-diffusion coefficients of 1H were measured using pulsed field gradient NMR (PFG-NMR) with the stimulated echo sequence. Self-diffusion coefficients were determined according to eq 2, with I and I0 the areas of the signals obtained with and without gradient pulses. The magnitude of the pulsed magnetic field gradient was varied between 0 and 23 T m−1; the diffusion time Δ between two gradient pulses was fixed to 20 ms, and the pulse duration δ was set to 1 ms. The π/2 radio-frequency pulse length was adjusted to 8.0 μs. All PFG-NMR experiments were performed at T = 25 °C. Electrophoretic NMR. Studies were carried out in a wide bore Oxford 4.7 T magnet using a Bruker Biospin NMR console operating at 200.1 MHz. Magnetic field gradients were generated using a diff60 diffusion probe and a Great60 gradient amplifier (Bruker Biospin). The diffusion time was typically 20 ms, and the gradient pulse width was 1 ms. During the E-NMR measurement the gradient strength was kept constant, and the applied electric field was varied. The electrophoretic NMR cell is in-house built and similar to the cell described by Hallberg et al.9 The electric field is generated in a 3 cm space between two platinum ring connected to a home-built dc amplifier which is driven by TTL pulses from the spectrometer and controlled with a customized pulse program. The time between two measurements was set to at least 5 s to avoid local sample heating which may lead to convection. All E-NMR experiments were performed at T = 25 °C. Conductivity Measurements. A cylindrical glass cuvette (length 15 mm, diameter 4 mm) with platinum disk electrodes was used for conductivity measurements of liquid samples. An opening at the top was used for filling and as an exit for residual gas bubbles within the cell. Conductivity measurements in pure water vapor (pH2O = 105 Pa) were carried out in a double-wall temperature-controlled glass chamber with an open outlet at temperatures between T = 110 and 150 °C. Liquid water was continuously evaporated by a heater and injected into the chamber with a constant flow rate using a digital peristaltic pump (Ismatec). Inside the chamber the samples pressed pellets of total thickness of 2−4 mm and 6 mm diameter were placed in a porous cylindrical tube gold electrodes. Complex impedance spectroscopy was carried out using a HP 4192A LF impedance analyzer in the frequency range 10−2−106 Hz using a voltage output of 0.1 V. Specific conductivities were obtained from the high-frequency intercept of the complex impedance with the real axis and the dimensions of the stacks. Small-Angle X-ray Scattering (SAXS). SAXS measurements were carried out on nominally dried pellets in the H+ form (diameter: 6 mm; thickness: 0.2 mm). The scattering experiments were performed by using a SAXSess camera (Kratky, Anton Paar) equipped with a CCD detector. Cu Kα radiation with a wavelength of 0.1542

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RESULTS AND DISCUSSION The proton conductivity of sulfonic acid functionalized membrane materials is well-known to increase with the concentration of ionic groups in a highly nonlinear fashion. This is especially true for low-humidity conditions where percolation within the aqueous conducting domain becomes a critical issue.32 For this reason, the increase of the local concentration of ionic groups within the conducting domain of phase-separated membranes (e.g., di-, tri-, and multiblock copolymers33−36) is thought to be an efficient strategy to obtain high conductivity under high-temperature, low-humidity conditions. In an attempt to push this approach to its limits, we have recently synthesized a fully aromatic polyelectrolyte with phenyl rings carrying four sulfonic acid groups.19 The comparatively low conductivity of this material, however, stands in contrast to its high ion exchange capacity of 7.04 mequiv g−1, raising the question which parameters control proton conductivity in environments with high concentrations of ionic (here sulfonic acid) groups. In order to separate the effects of counterion condensation from those of percolation and intermolecular interactions, we therefore consider the counterion condensation behavior of 1− 3 (Scheme 1) in dilute aqueous solutions as obtained from combined PFG- and E-NMR and from conductivity measurements. The results are then discussed in the light of Manning− Oosawa counterion condensation theory before including considerations about specific chemical interactions and microconformations. The diphenylene sMSO2-207 1 actually features one sulfonic acid functional group per phenyl ring, both in meta position with respect to the sulfone (SO2) linker, while the sulfones of D

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Macromolecules Table 1. Proton Dissociation of Sulfonated Monomer and Polymers by NMR Mn (g mol−1) 1: sMSO2-207 2: sPSO2-220 3: sPSO2-142

414 44000 5700

EW (g equiv−1)

no. of ionic groups zi

207 220 142

−6

5.84 × 10 1.99 × 10−7 2.05 × 10−6

2 200 40

exp

α (%)

9.30 × 10−5 5.72 × 10−5 2.30 × 10−5

100 61 25

α (%)

2 107 13

104 54 33

dissociated systems, μ approaches μ (∞); otherwise, the ratio between the two limiting values corresponds to the degree of dissociation of the system under consideration. This procedure is nothing but the determination of the number of ionic charge carriers with known mobility from a conductivity (σ = nqμ, with n being the number of charge carriers and q the unit charge). Since in this experiment, the conductivity only stems from protonic charge carriers (for 2 and 3 the conductivity contributions from the large polyanions are about 2 orders of magnitude lower), this method does not require the knowledge of Mn as is the case for the combined PFG-/E-NMR approach, in which diffusion and drift of polyanions are observed. The fact that the dissociation degrees obtained by both methods are quite close (compare values for α in Tables 1 and 2) gives us some confidence that the experimental data, especially for Mn, are reliable. As an example, Figure 3 shows the proton mobility μ expressed as conductivity diffusion coefficient Dσ = (kT/e)μ recorded on pressed pellets of sPSO2-22039 (open circles) and aqueous solutions (bold circles) over a wide range of water volume fractions. The conductivity diffusion coefficient remains about 40% below the limiting proton conductivity diffusion coefficient for aqueous media (9.31 × 10−5 cm2 s−1),38 indicating a degree of dissociation of α = 60%. Further support for counterion condensation comes from the data recorded at low water contents, where the samples are solid. Figure 3 also includes the water tracer diffusion coefficient DH2O recorded in

Dσ(H+) → ∞ (cm2 s−1) lit.

effective charge z

4.73 × 10−4 8.30 × 10−4 1.04 × 10−3

Figure 3. Room temperature diffusion (T = 25 °C) coefficients as a function of water volume fraction Φ for sPSO2-220. Orange points: conductivity diffusion coefficients Dσ, calculated via Nernst−Einstein equation from conductivity data assuming complete dissociation (open symbols−pellet measurements (taken form ref 39; filled symbols solution measurements). Blue points: water diffusion coefficients DH2O from PFG-NMR at T = 25 °C (data taken from ref 39). Proton diffusion coefficient at infinite dilution (red) is given as comparison. Lines are given to guide the eye.

Table 2. Degree of Proton Dissociation Derived from Conductivity Data

9.31 × 10−5

μ (cm2 V−1 s−1)

infinite dilution of the polyelectrolyte (obtained from the conductivity via the Nernst−Einstein relationship assuming full dissociation) with the limiting proton mobility μ (∞) as tabulated in textbooks38 (Figure 3). Only for completely

the corresponding monosulfonated poly(phenylene sulfone) sPSO2-220 2 has two nonequivalent sulfone linkers with either two sulfonic acid functions in ortho or in meta position (see Scheme 1). As a consequence, the latter shows at least two characteristic separations between neighboring sulfonic acid groups. The hypersulfonated poly(phenylene sulfone) sPSO2142 3 comprises 4,4′-diphenylene units which are octasulfonated; i.e., each available carbon carries an ionic group which is taking neighboring sulfonic groups to the closest possible proximity. While the separation of ionic groups is affected by conformational changes in the case of 1 and 2, the shortest separation of the four sulfonic groups on a given ring of 3 is fixed by the ring structure. Effective Charge of Polyelectrolytes As Determined by Combined PFG- and E-NMR. The number of charges z per object drifting in the electric field is obtained through eq 1. Comparing this number with the number of ionic groups per object as obtained from the equivalent weight and the molecular weight Mn (measured by gel permeation chromatography GPC) then yields the degree of dissociation α. The results as accessed by this experimental approach and summarized in Table 1 clearly suggest increasing counterion condensation) in the order 1−3. While the simple diphenylene 1 does not show any signature of counterion condensation, only about half of the protons of the corresponding polymer 2 appears to be separated from the polyelectrolyte in aqueous solution while the other half is involved in some counterion condensation. The latter observation appears to be quite interesting considering the fact that 2 is just a sequence of several units of 1. But as pointed out above, only 2 has sulfones with two sulfonic acid groups in the ortho position. Below, the discussion of the MD simulation results obtained for sPSO2220 will therefore have a special focus on this part of the polymeric structure. Counterion condensation behavior has already been observed by Scheler et al.37 with the same experimental approach applied on polycations as opposed to the polyanions used in this study. The very low degree of dissociation obtained for the polyelectrolyte containing fully octasulfonated biphenyl units is quite expected, since here the separation of neighboring sulfonic acid units is well below the Bjerrum length of water at T = 25 °C (0.71 nm). Proton Dissociation from Conductivity at High Dilution. An alternative method for obtaining the degree of dissociation α is the comparison of the apparent proton mobility μ as a function of concentration extrapolated to

1: sMSO2-207 2: sPSO2-220 3: sPSO2-142

Dt (cm2 s−1)

E

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Scheme 2. Sketches of Limiting Conformations with Respect to the Separation of Neighboring Sulfonic Acid Groups for Meta (a, b) and Ortho Form (c, d)a

a

Trans conformations (a, c) correspond to the maximum separation of ionic groups while cis conformations (b, d) take neighboring ionic groups to the closest possible distance. In the case of the ortho form, this allows for the formation of a bridging conformation involving two sulfonic anions and one cation.

values are smaller than the Bjerrum length of water at T = 25 °C (0.71 nm), and therefore, the observed counterion condensation properties of 2 and 3 are quite expected, with the hypersulfonated polyelectrolyte 3 being less dissociated than 2. Even in the case of the diphenylene 1, a closer look at the molecular structure (Scheme 1) reveals separations of the two sulfonic groups within the molecule which can be larger than the average separation in dry bulk material. This is because the two ionic groups are in meta position to the central sulfone group which allows the neighboring sulfonic groups to cover separations in the range from 0.53 (cis form, Scheme 2b) to 1.13 nm (trans form, Scheme 2a). In other words, there is a wide range of conformations with separations between the two sulfonic groups larger than the Bjerrum length (0.71 nm) consistent with complete dissociation as observed experimentally. Since 2 is just a polymeric sequence of the monomer 1, this consideration also holds for polyelectrolyte 2. In this case, however, sulfonic groups are in the ortho position to every other sulfone group. In the trans form (Scheme 2c), this corresponds to a separation of ionic groups of the order of the Bjerrum length (0.73 nm), but the cis form takes the two sulfonic groups as close as 0.41 nm (Scheme 2d). If the system were fully dissociated, electrostatic repulsion of the sulfonic group would surely favor the trans form. On the other hand, counterion (proton) condensation involving electrostatic stabilization of one proton between two close sulfonic groups may stabilize the cis form. The latter corresponds to a semineutralized situation, i.e., a degree of dissociation α ∼ 0.5, which is close to the experimental values (0.54, 0.61). For such short ion separations, however, Debye−Hückel approaches fail since they ignore not only details of the water structure and the structure of the ionic (sulfonic) group but also ion−dipole, dipole−dipole, and dispersive interactions. In addition, partially or fully neutralized ionic groups may still have stabilizing interactions with water which are not included in Manning’s and Oosawa’s theory, and the conformational changes of the backbone may have its own energetics. All of that is included in the molecular dynamics simulation presented in the next section. Since this produces all thermally accessible configurations, entropic effects are fully reproduced as well. Specific Interactions: Micro Conformation. Since the main reason for including classical all-atom MD simulations into the present study is to obtain a more detailed insight into the effects of micro conformation on the dissociation behavior of sulfonated poly(phenylene sulfones), relatively small systems (sulfonated diphenyls in meta and ortho form, see also Scheme 2) embedded in a large number (851) of explicit water

this water concentration range, and this is found to be higher than the apparent conductivity diffusion coefficient Dσ. Since in this water concentration regime the mobility of protonic charge carriers is closely related to water tracer diffusion40 (vehicle mechanism as opposed to structure diffusion prevailing at high water content), this observation is additional evidence for counterion condensation. For aqueous solutions of the diphenylene sMSO2-207 (1), it should be mentioned that the conductivity contribution of the relatively small anion (conjugated base) could not be neglected. We have therefore determined this through measuring its tracer diffusion coefficient by PFG-NMR and assuming two charges per monomer (z = 2). The fact that, with this value, the conductivity is fully explained with complete dissociation made further iterations dispensable. Only for the material with octasulfonated units (3), there is some difference in the values of α obtained by the two methods. This is most likely in the uncertainty of the molecular weight determination, as GPC result is not very accurate, especially for highly charged polyelectrolytes. Electrostatic Considerations. As outlined in the Introduction, the most prominent framework for describing counterion condensation is the Manning−Oosawa theory1,41 only considering electrostatic interactions within a most generalized description of a polymer with ionic groups. The polymer is simply considered to be an infinite thread with equidistant point charges as to reproduce the total ionic exchange capacity (IEC) immersed within a dielectric medium, the electrostatic interactions treated within the Debye−Hückel limit. Then, the onset of counterion condensation is predicted for the separation of neighboring ionic groups falling below the so-called Bjerrum length lB of the dielectric medium. The latter corresponds to a characteristic length at which the electrostatic energy of neighboring point charges e2/(4πεrε0lB) equals the average thermal energy kT; i.e., lB only depends on the dielectric constant εr and temperature T. Since εr usually depends on T, lB may decrease or increase with T (increase in the case of aqueous systems). The beauty of this theory is that it works apparently well in its most simple form, especially for aqueous media. In other words, this straightforward electrostatic approach seems to capture the dominant interaction controlling dissociation/ condensation phenomena of polyelectrolytes in polar media. In a qualitative way, this is also confirmed by the present study. Just from the IEC and the density of the water free polyelectrolytes, the separation of ionic groups is calculated to be 0.59, 0.60, and 0.52 nm for 1, 2, and 3, assuming equidistant separation (ionic groups forming a cubic lattice). All of these F

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reported by Paddison et al.42 for similar sPSO2 dimers in their protonic form albeit without water molecules present. The ab initio electronic structure calculation revealed a preference for the cis conformation, where the two sulfonic acid groups are located on the same side of the backbone. This finding is explained by a strong stabilizing interaction between the sulfonic acid groups that is absent in the trans conformation and cannot be accessed in any conformation for the meta form. Generally speaking, the results suggest that intermediate states are often particularly stabilized by an intricate balance of electrostatic, solvation, and configurational free energetics. It is worth noting that triple ions have also been observed in salt solution43 and ionic liquids44 where the position of ions is not constrained through their binding to an organic structure. Effects on the Nanomorphology. Empirically, there is a distinct correlation between the IEC of ionomers and polyelectrolytes and the characteristic correlation length of their nanomorphology in the hydrated solid form (e.g., membrane).39 With increasing IEC, water is more efficiently dispersed corresponding to a decreasing correlation length of primary polymeric objects separated by aqueous films. Speaking in terms of (polymer/water) phase separation, with increasing proximity of ionic groups on the polymer backbone, less rearrangement of hydrated ionic groups is needed for the solvation shells to coalesce and to form an ordered ionic structure driven by residual ionic interactions.32 For very high density of ionic groups, only minor local relaxation leads to defined structures reminiscent of the structure of inorganic hydrates.39 Corresponding diffraction patterns show narrow peaks at high scattering vectors q compared to the broad socalled “ionomer peaks” at low q characteristic for the diffraction patterns of typical ionomers such as Nafion (Figure 6). For sulfonated poly(phenylene sulfones), this morphological evolution with IEC is immediately apparent in the corresponding SAXS patterns (Figure 6) recorded at given relative humidity (RH ∼ 75%). While the ionomer peak of the sPSO2-

molecules have been investigated. For these, the distance between the sulfur atoms of neighboring sulfonic groups has been chosen as reaction coordinate r in the metadynamics approach explained above. In this way the total free energy change ΔF along this coordinate is obtained. The results show a higher configurational freedom in the region r/rmax ∼ 0.5−0.7 for the meta form compared to the ortho form where the conformation is constrained by the presence of a global minimum at r/rmax ∼ 0.62 (Figure 4). The

Figure 4. Global free energy of meta (red) and ortho form (blue) as obtained from metadynamics with the separation of neighboring sulfonic groups taken as reaction coordinate r/rmax. Note that the global minimum is more distinct in the case of the ortho compared to the meta form.

latter corresponds to a conformation in which both sulfonic groups interact with a single cation (Na+); i.e., a triple-ion is formed. Interestingly, this triple ion is surrounded by a wellstructured hydration shell, which most likely contributes to the stabilization of this “partially neutralized” state (Figure 5).

Figure 5. Conformations corresponding to the global free energy minima (see Figure 4) of the ortho (left) and meta dimer (right) as obtained from metadynamics. Sodium ions are blue, and dimers are represented as van der Waals spheres. Only sodium ions within a distance of 0.7 nm from the center of mass of the dimer and water molecules within 0.35 nm around the sodium ions are included. Figure 6. Small-angle X-ray diffraction patterns of sulfonated poly(phenylene sulfones) of different equivalent weights (IEC) at RH = 75% (λ ∼ 7). The so-called ionomer peak is getting sharper and is shifting toward higher q for increasing IEC up to a value of 4.55 mequiv g−1 (sPSO2-220) corresponding to a decreasing correlation length d. Further increase of the IEC reverses this trend; i.e., the ionomer peak broadens again its position shifting back to lower q. The patterns of sPSO2-220, -360, and -1014 are taken from ref 39. The SAXS pattern of Nafion39 is given for comparison.

Such a stable configuration with pairwise neutralized sulfonic acid groups (formation of triple ions) and one dissociated counterion per each pair is absent in the meta form. Here, the molecular structure does not allow for any conformation with the sulfonic acid groups being close enough to form such triple ions. With regard to the results for the preferred bridging configurations, it has to be noted that similar findings were G

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Macromolecules 1014 (IEC = 0.99 mequiv g−1; for detailed chemical structure see Supporting Information) SAXS pattern appears in the same q-range as that of Nafion, with increasing IEC (2.77 and 4.55 mequiv g−1 for sPSO2-360 and sPSO2-220) the correlation peak moves to larger q with decreasing peak width. This trend is reversed, however, when moving on to even higher IEC (sPSO2-142 with a formal IEC of 7.04 mequiv g−1) which is quite expected on the basis of the severely reduced dissociation of sPSO2-142 (3) with a high fraction (∼70%) of sulfonic groups being neutralized. It is important to note that the water content of the sample in terms of λ = [H2O]/[−SO3H] under these conditions is only about half of that of all the other ionomers and polyelectrolytes (see Supporting Information Figure S4). The hydration number λ usually varies only very little especially at moderate relative humidity, where the water uptake is governed by the hygroscopicity of the sulfonic acid group.45 Counterion condensation is actually expected to reduce hygroscopicity since a large part of the heat of hydration stems from the hydration of dissociated protons. The reduced water uptake of sPSO2-142 is therefore additional support for severe counterion condensation effects to occur in this highly sulfonated poly(phenylene sulfone). It is also worth noting that the evolution of the ionomer peak’s position mirrors this of the conductivity, which severely decreases when increasing the IEC from 4.55 mequiv g−1 (sPSO2-220) to 7.04 mequiv g−1 (sPSO2142) (see Supporting Information Figure 3). Implications for the Development of Ion Conducting Membranes. Since counterion condensation has an immediate effect on the number of ions available for conductivity, the findings and explanations presented in this work may be useful in the development of ion conducting membranes in general. Once the density of ionic groups reaches a point where the average separation of ionic groups is of the order of the Bjerrum length of the corresponding medium, the degree of counterion condensation obviously depends on details of the molecular structure and the accessible conformations of the polymer carrying the ionic groups. In the case of the commonly used perfluorosulfonic acid (PFSA) membranes, separation, length, and flexibility of the side chains terminated by the ionic (sulfonic) groups are therefore expected to become controlling parameters for dissociation at high IEC. The benchmark PFSA, Nafion by DuPont, has an IEC of ∼0.9 mequiv g−1 which corresponds to an average separation of ionic groups of about 0.95 nm well above the Bjerrum length of water. Within the phase-separated morphology of Nafion, however, the ionic groups accumulate at the interface of locally flat polymeric and aqueous domains46 with a reduced average separation of only 0.80 nm, which is virtually independent of the water content.47 This reduction seems to be related to the length and flexibility of the side chains, since so-called short side chain (SSC) PFSAs such as Aquivion by Solvay and the 3M membrane are less phase separated with a slightly larger separation of ionic groups at a given IEC.47 It therefore may be speculated that SSC-PFSAs are less prone to counterion condensation when increasing their IEC. For an even distribution of sulfonic acid groups, the Manning counterion condensation limit is expected to occur at an IEC of 2.17 mequiv g−1 corresponding to an equivalent weight of 461 g equiv−1 (calculated from the dry weight). With a reduction of the separation of ionic groups by about 10%, which is a typical value for PFSAs, this limit may be around 610 g equiv−1. The equivalent weights of PFSAs with the highest conductivities are actually of the same order (790 g equiv−1 for

Aquivion (Solvay) and 580 g equiv −1 for the 3M membrane;49,50 i.e., they are most likely close to the point where counterion condensation may become an issue. Another aspect, which is relevant for membranes but which does not play any role in solution, is the possibility of sulfonic groups of different polymer chains to getting close as well. In the case of Nafion, neighboring polymeric objects are suggested to be separated by water films getting thinner with decreasing water content. The average thickness of such films falls below the Bjerrum length at a hydration number of λ ∼ 7.46 It is interesting to note that this is the water concentration where the activation enthalpy of ionic conductivity starts to markedly increase. It may be speculated that, in this regime, a large number of weakly solvated ionic species are involved in weak condensation processes leading to some ordering and decrease of ionic mobility. Even for larger water contents (λ > 7) weak residual ionic interaction is held responsible for the evolution of flat morphologies (up to λ ∼ 28). The weak ion condensation processes going along with this ordering may only occur in membranes but not in solution. The present results also suggest that counterion condensation on a given polymer strand starts with the pairwise neutralization of sulfonic groups, i.e., the formation of triple ions leaving half of the cations mobile. Similar complexes are also thought to occur in anion exchange membranes with higher separation of ionic groups.51 In this case, the immobilized cation is a moderately basic quaternary ammonium with chloride being the counterion. One therefore must keep in mind that the onset of counterion condensation may not only be controlled by the nature of the solvent but also by the chemical nature of the immobilized ionic group and the corresponding counterion. Coming back to sulfonic acid functionalized systems, this implies that the onset of proton condensation may also depend on the way the sulfonic group is attached to the polymer structure.52 With the strong electronwithdrawing effect of CF2 groups, PFSA membranes may be less prone to counterion condensation than sulfonated hydrocarbon membranes. The most direct implications of the present work are surely those which relate to the development of membranes based on sulfonated poly(phenylene sulfones) which are among the few hydrocarbons with the potential to outperform available PFSAs. More than for PFSAs, the IEC must be increased to the limit where maximum conductivity is achieved in structures in which the ionic groups are constrained to a volume increment providing conductivity while another part of the structure provides the membrane materials with acceptable morphological stability. This may be the case for block structures with one block being a sulfonated poly(phenylene sulfone)34 or specific blends with an inclination to phase separate.53 One of the reasons to concentrate the sulfonic groups in parts of the membrane structure is the fact that the conductivity increases with IEC in a highly nonlinear fashion (Figure 7 and Supporting Information Figure S4). But this is only true up to a point where counterion condensation is starting to occur while percolation within the aqueous phase is getting less of an issue. Among the conductivity data, shown in Figure 7, the conductivity of sPSO2-220 appears to be the highest with a value only about a factor of 2 lower than that of a water-soluble PFSA with an equivalent weight of 580 g equiv−1.49 As shown in this work, this conductivity is already affected by some counterion condensation bridging adjacent sulfonic groups in meta position H

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Macromolecules

applied electric field for sPSO2-142 and sMSO2-207, phase shift of polymer 1H signal for different magnetic gradient strengths, 1 H signal phase shift of residual H2O for different magnetic gradient strengths, proton conductivity of sulfonated polyelectrolytes at pH2O = 1 atm, hydration isotherms at 65 °C of sulfonated polyelectrolytes, condensation constant Kc(r) and number of contacts between sodium and oxygen atom of allatom MD simulations for meta and ortho sulfonated dimers and the molecular weight distribution by GPC of sPSO2-220. This material is available free of charge via the Internet at http:// pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail [email protected] (A.W.). *E-mail [email protected] (K.-D.K.).

Figure 7. Proton conductivity of sulfonated poly(phenylene sulfones) at T = 120 °C, RH = 50% as a function of IEC; lines are shown to guide the eye.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We kindly acknowledge the Bundesministerium für Bildung and Forschung, Energie Baden-Wuerttemberg EnBW, and Fumatech for financial support (project PSUMEA 03ET2004A) and the cluster of excellence ‘Simulation Technology’ (CEX 310) for financial support. The authors thank Uwe Traub and the electronic workshop of MPI for solid state research for helping to set up the electrophoretic NMR equipment and Giorgi Titvinidze, Jan Melchior, Michael Marino, Anand Narayanan Krishnamoorthy, and Christian Holm for useful discussions.

to a sulfone group. Separating these two ionic groups through an additional unsulfonated phenyl ring may be one possible measure to suppress counterion condensation and further increase conductivity. One must also keep in mind that the flat water structures in sPSO2-220 are very narrow which may also favor some ion condensation (see Nanomorphology section). The fact that the activation enthalpy of proton conductivity is distinctly higher than that of PFSAs even at very high water content could be another signature of ionic ordering (condensation).39 Generally speaking, the regime close to where counterion condensation occurs may be particularly suitable for obtaining interesting combinations of conductivity, selectivity, and water uptake. This is relevant not only for the optimization of membranes for fuel cells but also for other electrochemical and chemical applications such as flow batteries, electrodialysis, and reverse osmosis.

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(1) Manning, G. S. J. Chem. Phys. 1969, 51, 924−933. (2) Böhme, U.; Scheler, U. Adv. Colloid Interface Sci. 2010, 158, 63− 67. (3) Wong, S.; Scheler, U. Colloids Surf., A 2001, 195, 253−257. (4) Stejskal, E. O.; Tanner, J. E. J. Chem. Phys. 1965, 42, 288−292. (5) Packer, K. J. Mol. Phys. 1969, 17, 355−368. (6) Holz, M.; Lucas, O.; Müller, C. J. Magn. Reson. 1984, 58, 294− 305. (7) Saarinen, T. R.; Johnson, C. S. J. Am. Chem. Soc. 1988, 110, 3332−3333. (8) Ise, M.; Kreuer, K. D.; Maier, J. Solid State Ionics 1999, 125, 213− 223. (9) Hallberg, F.; Weise, C. F.; Yushmanov, P. V.; Pettersson, E.; Stilbs, P.; Furó, I. J. Am. Chem. Soc. 2008, 130, 7550−7551. (10) Böhme, U.; Scheler, U. Chem. Phys. Lett. 2007, 435, 342−345. (11) Griffiths, P. C.; Paul, A.; Stilbs, P.; Petterson, E. Macromolecules 2005, 38, 3539−3542. (12) Zhang, Z.; Madsen, L. A. J. Chem. Phys. 2014, DOI: 10.1063/ 1.4865834. (13) Bielejewski, M.; Giesecke, M.; Furó, I. J. Magn. Reson. 2014, 243, 17−24. (14) Hallberg, F.; Furó, I.; Yushmanov, P. V.; Stilbs, P. J. Magn. Reson. 2008, 192, 69−77. (15) Håkansson, B.; Nydén, M.; Söderman, O. Colloid Polym. Sci. 2000, 278, 399−405. (16) Schuster, M.; Kreuer, K. D.; Andersen, H. T.; Maier, J. Macromolecules 2007, 40, 598−607. (17) Schuster, M.; de Araujo, C. C.; Atanasov, V.; Andersen, H. T.; Kreuer, K. D.; Maier, J. Macromolecules 2009, 42, 3129−3137. (18) Atanasov, V.; Buerger, M.; Wohlfarth, A.; Schuster, M.; Kreuer, K. D.; Maier, J. Polym. Bull. 2012, 68, 317−326. (19) Takamuku, S.; Wohlfarth, A.; Manhart, A.; Raeder, P.; Jannasch, P. Polym. Chem. 2014, DOI: 10.1039/C4PY01177E.

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FINAL REMARKS Once the density of ionic groups (−SO3H) of polysulfones reaches a point where their average separation is of the order of the Bjerrum length of water, the degree of counterion condensation is shown to depend on details of the molecular structure and the accessible conformations of the polymer carrying the ionic groups. In this regime, well-defined ionic aggregates (here: triple ions) occur leading to local minima in the global free energy landscape. For describing the latter, details of the molecular structure and conformations including their degrees of freedom and specific interactions between ions and solvent and among ions are shown to critically affect the dissociation behavior of sulfonated polysulfones. When it comes to ion conducting membranes, increasing the ion exchange capacity (decreasing the average separation of ionic groups) is a common measure to increase ionic conductivity. The present results clearly show that the limit of this approach depends on the accessible conformations, in particular on how close the sulfonic acid groups may approach.

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REFERENCES

ASSOCIATED CONTENT

S Supporting Information *

Chemical structures of sPSO2-360 and sPSO2-1014, PFG-NMR spin-echo 1H signal attenuation of sPSO2-220, sPSO2-142 and sMSO2-207, linear trend of the phase angle as a function of the I

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