Binding of Monovalent and Multivalent Metal Cations to

Article pubs.acs.org/JPCB

Binding of Monovalent and Multivalent Metal Cations to Polyethylene Oxide in Methanol Probed by Electrophoretic and Diffusion NMR Marianne Giesecke, Fredrik Hallberg, Yuan Fang, Peter Stilbs, and István Furó* Division of Applied Physical Chemistry, Department of Chemistry, KTH Royal Institute of Technology, SE-10044 Stockholm, Sweden S Supporting Information *

ABSTRACT: Complex formation in methanol between monodisperse polyethylene oxide (PEO) and a large set of cations was studied by measuring the effective charge acquired by PEO upon complexation. Quantitative data were obtained at a low ionic strength of 2 mM (for some salts, also between 0.5 and 6 mM) by a combination of diffusion nuclear magnetic resonance (NMR) and electrophoretic NMR experiments. For strongly complexing cations, the magnitude of the acquired effective charge was on the order of 1 cation per 100 monomer units. For monovalent cations, the relative strength of binding varies as Na+ < K+ ≈ Rb+ ≈ Cs+, whereas Li+ exhibited no significant binding. All polyvalent cations bind very weakly, except for Ba2+ that exhibited strong binding. Anions do not bind, as is shown by the lack of response to the chemical nature of anionic species (perchlorate, iodide, or acetate). Diffusion experiments directly show that the acetate anion with monovalent cations does not associate with PEO. Considering all cations, we find that the observed binding does not follow any Hofmeister order. Instead, binding occurs below a critical surface charge density, which indicates that the degree of complexation is defined by the solvation shell. A large solvation shell prevents the binding of most multivalent ions.

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interaction of N-methylacetamide with alkali halides8 by MD simulations. In this study, we focus on polyethylene oxide (PEO, also known as polyethylene glycol (PEG)) and its interaction with different cations. PEO is a polymer of broad interest, both because of its various commercial applications and for its use as a model for uncharged water-soluble polymers. In the last few decades, a lot of research concerning PEO was directed toward its role as a solid polymer electrolyte in applications such as fuel cells, batteries, and solar cells.9 PEO has the ability to dissolve ionic salts, yielding a material with high conductivity. A majority of studies have focused on the alkali metal salts with particular attention given to lithium. The cation is thought to coordinate the ether oxygen of the polymer; however, the mechanism of ion transport10 is not fully understood. The interaction of PEO with ions in solution has also practical consequences, with examples ranging from the behavior of PEGylated surfaces in drug delivery11 to nanopore probing of molecules.12 The interactions between small cations and linear PEO are known to be weak in aqueous solutions.13 In contrast, these interactions are more prominent in nonaqueous solutions where they have been studied quite extensively.14−16 Interesting

INTRODUCTION Specific ion effects that cannot be explained by theories of classical physical chemistry are often denoted by the term “Hofmeister effects”.1,2 Initially, Hofmeister described the influence of salts on the precipitation of proteins in water; however, such phenomena can also be observed in nonaqueous solutions3 and in many different types of systems and interfaces. In recent years, a vast number of studies have focused on revealing the mechanisms behind these specific ion effects; a majority of investigations considered the specific (yet slightly phenomenon- and system-dependent) order exhibited by anions, although cations can also be arranged in a Hofmeister series. Because of the lack of a comprehensive model that would include all ion interactions and predict their behavior in a given system, a common approach has been to try to correlate experimental data with physicochemical properties characteristic of the ions investigated.4 For example, one of the theories that has emerged for simple ions is the law of matching water affinities that states that ions of opposite charge with similar size and water affinity show a stronger attraction than dissimilarly sized ions in water.5 Biomolecules6 and polymers are among the most studied systems that exhibit Hofmeister effects. Concerning noncharged polymers, many show interesting ion association phenomena. Recent work on polymers includes the interaction of poly N-isopropylacrylamide with sodium salts with different counteranions7 as well as the © 2016 American Chemical Society

Received: September 3, 2016 Revised: September 13, 2016 Published: September 13, 2016 10358

DOI: 10.1021/acs.jpcb.6b08923 J. Phys. Chem. B 2016, 120, 10358−10366

Article

The Journal of Physical Chemistry B

the experiments were repeated with acetate and iodide salts. Additional samples of 2 mM acetate salts in methanol were prepared to study the ion pairing behavior of the salt alone. Most experiments were performed at cPEO = 2 mM and csalt = 2 mM. In addition, for four selected cations (K+, Ca2+, Ba2+, and Al3+), experiments were also performed at 0.5 mM metal ion concentration with 0.5 mM monomeric PEO concentration, whereas for K+ and Ba2+, we performed experiments also at 0.5 and 6 mM metal ion concentrations with 2 mM monomeric PEO concentration. Some of the salts and PEO contained water that could not easily be removed and some samples adsorbed water from natural atmospheric humidity during the eNMR experiments. Hence, a small yet controllable water content (of 120 ± 20 mM) was therefore chosen and initially set in all samples so that the variation of water content among samples and during experiments was negligible.30 In addition, others have shown that adding water up to 0.1 v/v to methanol has a negligible effect on ion association behavior.31 Additional experiments, where the water concentration was varied, were performed and are summarized in the Supporting Information (SI). All 1H diffusion and eNMR experiments were performed on a 500 MHz Bruker Avance spectrometer equipped with a highresolution probe with z-direction gradient coils (providing a maximum gradient of 50 G cm−1) at 298.7 K. The 5 mm eNMR cell previously described,32 with a distance of approximately 36 mm between electrodes, was used in all experiments. In the NMR diffusion experiments, a doublestimulated echo pulse sequence33 was used. The amplitude g of the pulsed field gradients was stepped up linearly from 0.5 to 33 G cm−1 in 24 steps. The duration of the gradient pulses, δ, and the total diffusion time, Δ, were set to be 3 and 400 ms, respectively. For each PEO sample containing an acetate salt, an additional diffusion experiment was performed to obtain the diffusion coefficient of the acetate ion accurately. In this measurement, the amplitude g of the pulsed field gradients was stepped up linearly from 1 to 20 G cm−1 in 24 steps and with δ and Δ set to 3 and 200 ms, respectively. Diffusion coefficients were obtained by fitting a Gaussian decay

differences between solvents have been evidenced, for example, Li+ was found to remain free in aqueous solutions and in methanol, whereas it was bound to PEO in acetonitrile.16,17 Particularly in methanol, large differences among cations in their complexation with PEO have been reported.18−21 The degree of association with PEO has been found in conductometric studies to increase along the series of alkali metal ions according to Li+ ≪ Na+ < K+ ≈ Rb+ ≈ Cs+.22,23 It has also been reported that Ba2+ binds more strongly than Sr2+ among divalent cations.19,20 Yet, experimental techniques and conditions and, particularly, the sometimes complex models used have varied between studies, and therefore it remains difficult to make quantitative comparisons. This calls for systematic and preferably quantitative studies including, ideally, all relevant ions previously investigated; one then hopes to observe trends that may have remained hidden. Performing experiments at a sufficiently low salt concentration is also desirable, so that the effects of solvent activity can be neglected and that of ion−ion interactions16,24,25 can be minimized. Preferably, the study should also rely on a conceptually simple method, whose evaluation is not excessively model dependent. Hence, in this work, the interactions between a large set of cations, including several divalent and trivalent cations, and PEO in methanol were studied by a combination of electrophoretic and diffusion nuclear magnetic resonance (NMR). To address the behavior of the anions in the polymer−salt system, the study was extended to several counteranions for the salts used. As has been shown, the combination of diffusion NMR and electrophoretic NMR (eNMR) experiments allows the direct determination of the effective charge of ions and molecules in solution.26−29 In contrast to other experimental methods, this can be done directly without titration of any component. In another contrast to, for example, binding studies based on conductometry, ultrafiltration, and ion-selective electrodes,13,18−21 where binding is assessed by measuring the often rather small change caused by the reduction in the number of free ions, we directly estimate the number of charges attached to the polymer. Typically, one expects direct methods to be more accurate than indirect ones based on depletion effects. Moreover, the effective charge is a binding parameter that is relatively easy to interpret (e.g., compared to conductivity data, where complex models have to be applied to derive binding constants). As the sign of the charge is experimentally obtainable from eNMR, it is straightforward to decide whether mainly anions or cations associate with the uncharged molecule. One of the counteranions used in this study is the acetate ion, which has the advantage of providing a 1H signal. In this way, the behavior of that anion can also be monitored.

⎧ ⎛ δ ⎞⎫ S = exp⎨−γ 2δ 2g 2D⎜Δ − ⎟⎬ ⎝ ⎩ S0 3 ⎠⎭

(1)

to the variation of the acquired NMR spectral integral of the PEO, where S and S0 are the integral intensities with and without gradient and γ is the magnetogyric ratio.34 The obtained diffusion data together with the estimated error are summarized in the SI. The gradient strength was calibrated using the known value of the trace 1H diffusion coefficient in heavy water.35 In eNMR experiments, a double-stimulated echo pulse sequence with bipolar electrophoretic voltages36 was used. The electric field E was stepped up from 0 to a maximum of ±55.6 V cm−1 in at least 8 steps while all other parameters were kept constant. The duration δ and amplitude g of the gradient pulses were 1 ms and 20 G cm−1, respectively, whereas the drift time ΔE was set to 200 ms. The previously described reference phase correction method32 was used to obtain the electrophoretic mobilities. In this method, the phase difference between the target molecule and an uncharged reference molecule, such as methanol here, compensates for bulk flow effects caused by electro-osmosis and thermal convection.32,37 For samples containing 2 mM acetate salts in methanol (without the

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EXPERIMENTAL SECTION A stock solution of PEO (Mw = 22 000 g mol−1 and polydispersity index Mw/Mn = 1.10, chains of approximately Np = 500 monomeric units, Polymer Source) was prepared. Metal perchlorate ClO4−, iodide I−, and acetate CH3COO− salts (>99% purity) and methanol-d4 (>99.8% D), all from Sigma-Aldrich, were used as received. Samples probed in experiments contained PEO at cPEO monomeric concentration and one selected salt adjusted to csalt metal ion concentration and 120 ± 20 mM H2O in deuterated methanol-d4. The effective charge of PEO was measured for 12 different perchlorate salts (with monovalent, divalent, and trivalent cations). For five selected cations (Li+, K+, Cs+, Ca2+, and Ba2+), 10359


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The Journal of Physical Chemistry B polymer), E was stepped up from 0 to a maximum of ±111.1 V cm−1 in 10 steps, whereas δ, g, and ΔE were set to 1 ms, 13 G cm−1, and 200 ms, respectively; the resulting spectra are shown in Figure 1a. A slight temperature increase due to Joule heating

molecules), on the other hand (see Figure 1a), with increasing electric field. The increasing phase of the PEO signal is visualized by the increasingly dispersive shape gained by that particular peak (see Figure 1a) upon increasing the electric field.

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RESULTS AND DISCUSSION The effective charges of PEO for various perchlorate, iodide, and acetate as counteranion via eq 3b using the electrophoretic mobility coefficient values (see SI) and are presented

cations with are calculated and diffusion in Figure 2.

Figure 2. Effective charge z of PEO with metal ion perchlorate, iodide, and acetate salts added, as estimated by eNMR and diffusion NMR experiments at 2 mM monomer concentration of polymer and salt concentration in methanol-d4. For K+, Ca2+, Ba2+, and Al3+ ions with perchlorate anions, data are presented also at 0.5 mM equimolar concentration. The representative compounded experimental error, see detailed discussion in the SI, is illustrated by the single error bar given for the K+-perchlorate data column. Figure 1. (a) 1H NMR spectra with increasing electric field over a sample containing PEO (2 mM monomeric concentration) and CsI (2 mM) in methanol-d4. Observe the increasing phase shift of the PEO peak (at approximately 3.8 ppm) with increasing electric field, manifested by its increasingly dispersive line shape. The inset shows the PEO peak at zero and at maximum electric field. The extracted quantity is the phase of that peak ϕ relative to that exhibited by the methanol and water peaks (3.4 and 4.9 ppm, respectively, with very small phase changes) that originate from uncharged species. (b) Variation of phase ϕ for the PEO peak with increasing electric field strength E, as extracted by direct phasing of the PEO peaks in the spectral series in (a). The error bars represent the estimated ±2° error in the phasing process. The slope of the line provides, via eq 2, the electrophoretic mobility μ = 16.9 × 10−9 m2 V−1 s−1.

Clearly, the effective charge is highly dependent on the identity of the cation. The obtained effective charges are positive, and thereby it is also clear that the cation association with PEO is dominating.39 The section below is divided into several subsections. In the first of those, we investigate the state of the PEO in methanol and also show that the model with which we develop our quantitative results, the effective charge of the PEO chain that appears upon ion binding, is valid. In this section, we rely just on the magnitude of the observed ion binding. We also investigate the concentration dependence of the obtained binding constants and relate the observation to some theoretical considerations. Then, we investigate the observed variation over ions in detail and relate them to previous data. Finally, we seek to explain the observed trends in terms of physical parameters of the involved cations. PEO Chain in Methanol and Derivation of the Effective Charge of the Polymer−Ion Complex. The state of PEO in methanol has been studied in detail.15,40−43 Hence, there is conclusive evidence that methanol is between being a theta solvent and a good solvent44 for a PEO chain of intermediate length (6000 < Mw < 106 g mol−1). In particular, the Mark−Houwink exponent a was indicated by various studies15,40−43,45,46 to be in the range of a ≈ 0.51−0.62 in the temperature range of 298−303 K and the theta temperature was determined to be ca. 330 K,46 far above the temperature

was noted in the eNMR experiments. (To calculate the correct effective charge (see below) the obtained diffusion coefficients were corrected for this by exploiting the known temperature dependence of the viscosity of the solvent.38) Electrophoretic mobilities, summarized (together with the estimated error) in the SI, were obtained by fitting a straight line (see Figure 1b) to the electrophoretic modulation32 ϕ = γgδ ΔEμE

(2)

of the NMR signal phase difference ϕ between the PEO peak (target molecule), on the one hand, and either the methyl peak of methanol or the water peak (both uncharged reference 10360


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sufficiently low so that the obtained binding trend over this ionic series is significant. In this context, our explored concentration is among the most dilute ones (indeed, 0.5 mM is the most dilute system investigated). From the observed effective charges, one can obtain the number of bound ions as

explored here (298.7 K). Hence, our PEO chain is in an extended state with the global shape of a random coil. Indeed, our obtained diffusion coefficient DPEO = 8 × 10−11 m2 s−1 in salt-free solution supports this conclusion; it yields, via the Stokes−Einstein relation DPEO = kBT/6πηrPEO, a hydrodynamic radius that is rPEO = 4.7 nm (kB represents the Boltzmann factor, T the absolute temperature, and η the viscosity of the solvent methanol). Within this radius, the volume fraction of an Mw = 22 000 g mol−1 PEO chain is of the order of 10%. Upon ion binding, the PEO chain attains a charge and thereby exhibits a nonzero electrophoretic mobility. Formulated in another manner, the force exerted by the applied electric field on the positive charges moves the polymer if those charges are bound to the polymer sufficiently strongly. Indeed, this has been explored for investigating the binding of PEO to charged micelles by eNMR.47 As is shown in Figure 2, the maximum excess positive charge bound to our current PEO chains is ca. 5−6. Considering the hydrodynamic radius, this yields, at most, a local excess counteranion concentration of ca. 20 mM (considering the polymer chain length, another measure of ion concentration is approximately 1 elementary charge per 100 monomer). In other words, the ion binding creates a weak polyelectrolyte. The behavior of such a polyelectrolyte in an electric field48 is not well represented by solid-particle-like models where the charge is represented by a charge density distributed evenly on the particle surface. Indeed, ions bound to PEO chains continue to behave as discrete charges that are surrounded and screened by freely moving and monovalent anions and solvating methanol molecules, just like ions in the free state with the only difference that the effective anion concentration may shift from 2 to a maximum of ca. 20 mM. (The actual anion concentration may be significantly lower if confinement effects lead to electroneutrality being broken down within the polymer chains.49) At the latter (and clearly overestimated) anion concentration (having a free cation concentration as that of the bulk, that is 2 mM), the Debye screening length κ−1 for any of the solutions involved is larger than ca. 1.4 nm (see the SI), which in turn is much larger than any of the ionic radii rion. Hence, the individual PEO-complexed cations interact with an undistorted electric field.50,51 As a result, one retains (i.e., with correcting terms of less than a few percent) the Nernst− Einstein relation48

D=

μkBT ze

nbound =

kBT μPEO e DPEO

(4)

where zcation is the nominal cation charge (as discussed below, this may lead to some underestimation in the case of Ba2+). Thereafter, the equilibrium binding constant K is obtained as K=

ccomplexed ion (c PEO/Nb − ccomplexed ion)(csalt − ccomplexed ion)

(5)

In this expression, Nb is the size of the binding site in terms of the number of monomers. We chose here to use Nb = 6, a figure that seems to be consistent with most previous studies.22,39,52−55 The concentration of the complexed ions is simply obtained as ccomplexed ion = (nbound/Np)cPEO (where Np = 500, see above). The obtained binding constant data for all samples are presented in the SI. Having ca. 5 cations (as for K+, Rb+, and Cs+) bound to this system sets the average cation−cation distance to ca. 5 nm. This can be obtained by considering the average end-to-end distance of those approximately 80-monomer segments that separate the bound ions (the monomer length56 of PEO is 0.36 nm). The same conclusion can also be arrived at by considering the distance between spatially randomly placed points in a volume set by the ca. rPEO ≈ 5 nm hydrodynamic radius of the polymer (see above). Compared to this value, the bulk screening length κ−1 (at the 2 mM bulk concentration, ca. 4.5 nm for monovalent and 2.5 nm for divalent metal ions, see the SI) is not negligible. Hence, one expects the ion binding to be influenced by ion−ion interactions. Regarding the trends presented in Figure 2, the relative order among monovalent cations is not influenced, as they exhibit identical electrostatic behavior. Considering the relation between cations of different valencies, we first investigated whether the binding trends hold at a lower (0.5 mM) equimolar concentration. As shown by the data in Figure 2, for Ca2+ and Al3+, negligible binding is retained, whereas for K+ and Ba2+, one obtains roughly the same effective charge. The same effective charge at a lower salt concentration shows that K is, indeed, concentration dependent. Hence, it remained to be investigated if this concentration dependence is sufficiently different for monovalent cations and for Ba2+ for rendering their binding qualitatively different. The experimental concentration dependence of K for K+ and Ba2+ is shown in Figure 3. As there were some indications in some studies13,57 that K also depends on the PEO concentration, we made measurements at two selected PEO concentrations, 0.5 and 2 mM. Our results in Figure 3 show that K, at such low concentrations, does not depend on the concentration of PEO. A rough assessment of Figure 3a indicates that the binding for K+ and Ba2+ remains in the same order irrespective of the concentration, and the qualitative trend presented in Figure 2 holds. More quantitative comparisons can be made by investigating the data in the framework of theoretical considerations. Although all aimed at investigating the effect of ion−ion interactions on the weak polyelectrolytes that are created by ion binding, current theories differ regarding both formulation and tractability.16,24,25,57−59 In particular, an

(3a)

connecting via the effective charge z, the self-diffusion coefficient D, and the electrophoretic mobility μ, where e represents the elementary charge. In turn, this relation can then be used to estimate z PEO =

z PEO zcation

(3b)

the charge (in units of the elementary charge e) that has been bestowed upon the originally uncharged polymer by association with the ions. Note that even if the PEO molecule with bound ions is considered as a particle with a corresponding surface charge density, evaluating the effective charge via eq 3a yields a less than 10% error (i.e., the deviation of the Henry function50 at κrPEO ≈ 1 from its value at low ionic strength). Binding Constants and Ion−Ion Interactions. We investigate here whether or not the salt concentration is 10361


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Table 1. Self-Diffusion Coefficients D, Electrophoretic Mobilities μ, and Effective Charges z (See Equation 3a) of the Acetate Ion in 2 mM Salt Solution in Methanol-d4a salt LiAc KAc CsAc Ca(Ac)2 Ba(Ac)2

Dacetate (10−10 m2 s−1) 9.94 9.97 10.3 8.73 9.66

(10.33) (10.12) (10.17) (8.51) (8.79)

μacetate (10−8 m2 V−1 s−1) −3.62 −3.29 −3.81 −0.54 −1.03

(−3.65) (−3.44) (−3.58) (−0.66) (−1.17)

zacetate −0.94 −0.85 −0.95 −0.16 −0.27

(−0.91) (−0.87) (−0.9) (−0.20) (−0.34)

a

In parentheses, the respective values are given for the acetate ion in a solution that contains in addition PEO (at 2 mM monomeric concentration).

straightforward data collected here, we can state that anion binding to PEO in systems with monovalent cations is not significant in relation to the binding of the cations. This is in clear contradiction to some previous indications.15,20 Anions in water, though at 103-fold higher concentrations, have also been indicated to bind to PEO.60,61 Yet, our preliminary data (to be published elsewhere) recorded in aqueous solution at ∼mM salt concentration show no significant acquired charge for PEO. Indeed, high-concentration anions were indicated to influence PEO and its behavior via changing the activity of and molecular interactions with the solvent.16,62,63 The data in Table 1 also reveal that for monovalent cations, there is no significant ion pairing (as expected in methanol30,64) between the cations and anions. Hence, approximating the number of bound cations by nbound = zPEO is then a good approximation (see the derived equilibrium binding constants in the SI). For multivalent ions, ion pairing28,65 in neat methanol is clearly important, as is shown by the low effective charge of the acetate ion in such solutions. Hence, binding of charged ion pairs to PEO cannot be excluded. However, zPEO is very small for all multivalent ions except for Ba2+, and therefore the data in Figure 2 also indicates negligible binding for those. In addition, for Ca(Ac)2, the acetate diffusion coefficients with and without PEO coincide within the ca. 2% experimental error. Hence, eq 4 may yield a significant error for Ba2+. Because the acetate diffusion coefficient with PEO is significantly lower than that without PEO, there is clearly some association of acetate with the polymer, and the most plausible explanation is that some Ba2+ ions bind to PEO in the form of BaAc+ ion pairs. Indeed, such a binding mode was suggested by Ono et al. on the basis of NMR19 and conductivity measurements.20 Hence, approximating nbound = zPEO/2 for Ba2+ (as is done in Figures 3 and 4) can significantly underestimate the number of Ba2+ ions bound, with or without having acetates associated with, to PEO. Irrespective of this complication, the outlier behavior of Ba2+ with respect to the other multivalent ions remains and no conclusion drawn from Figure 4 (see below) is influenced by this effect. Comparing our data quantitatively to that by Ono et al. is not straightforward because different concentration ranges19 as well as different counteranions20 were used. Our results for monovalent ions show a similar trend to the one found in conductivity studies,22,23 even though the charges obtained by evaluating conductivity data within specific models were (by a factor of 2−4) higher than the charges found in the present investigation. The reasons for discrepancy were analyzed before in terms of shortcomings of the conductivity models and propagated experimental uncertainties.21 In

Figure 3. (a) Equilibrium binding constants for K+ and Ba2+ cations as obtained via eq 5 from data recorded at different salt and polymer concentrations. (b) Same data in (a) plotted as a function of the inverse screening length and fitted by exponential functions as given by eq 6.

exponential decay of K with increasing κ was predicted.16,24 Hence, the data in Figure 3b were fitted as K = K 0 exp( −λκ )

(6)

where theory suggests λ = lB/2, where lB is the Bjerrum length. The fits provided K0 = 390 for K+ and K0 = 260 for Ba2+, where K0 is the binding constant in the absence of ion−ion interactions. Hence, the binding of those two ions is, indeed, of comparable strength. Yet, the obtained exponents are far larger than lB/2, particularly so for K+ (see SI). This feature may require additional studies in the future. Cation Binding to PEO: Analysis and Comparison to Previous Data. Although cation association with PEO is the dominating feature,39 the anions dissolved in methanol may also associate. To evaluate to which minor degree this may happen,15,16,20 we have two observations to rely on. First, as is clear from Figure 2, changing the anion has only small (of the order of 10%) effects on the effective charge. In addition, in Table 1 we present the data obtained for the acetate anion in solutions with and without PEO. One can see that, for any monovalent cation, the acetate diffusion coefficient is not influenced by the presence of PEO, which explicitly excludes the possibility of any significant association between acetate anions and PEO. Hence, on the basis of the rather 16,24

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10−11 m2 s−1). Hence, ion binding seems to increase the hydrodynamic radius slightly, as expected for weak polyelectrolytes. The only exception to this trend was shown by Ba2+ at 6 mM salt concentration, where the diffusion coefficient became ca. twice higher than that at a lower concentration. This indicates a polymer that shrank into a tighter conformation with a smaller hydrodynamic radius, which in turn points to reorganization of the chain around that bound ion. Because at the same time the effective charge seems to decrease, this behavior is seemingly counterintuitive and may be a consequence of increasing pairing with anions. This feature will be subjected to further studies. Ion Properties Governing the Binding Behavior. Two of the most fundamental properties that cations may be characterized by are their charge and size. As most of the monovalent cations are bound to the polymer, one may expect that the binding should be even more pronounced among the polyvalent cations due to their higher charge. Yet, only Ba2+ seems to bind to PEO, thereby binding is not governed directly by the cation charge. Although the charge of an ion is readily defined, the ionic radius is not; its experimentally evaluated size depends on the atoms proximate to the ion and on the actual experiments that are used to assess size. However, there exists a comprehensive review74 whose ionic radii selected are widely used (see Table 2). Irrespective of the exact values of ionic

Figure 4. Estimated number of ions bound to PEO nbound (see eq 4) in the presence of perchlorate salts and correlated with the surface charge density (see eq 7) of the cation.

addition, the concentration ranges were often higher in conductivity-based studies. The complexation of cations to PEO has also been studied indirectly by measuring the electro-osmotic flow of saline methanol solution inside PEO-coated capillaries.18 The flow increased in the order Li+ < Na+ < Cs+ < K+, which is the same order as the one obtained for the complexation of PEO in this work. Furthermore, the flow was approximately equal for Ba2+ and K+ but considerably smaller for Ca2+ and Mg2+. It is interesting to note that binding of Li+ is clearly disfavored.16 In gas phase, in the absence of solvation effects, it was found that Li+ binds most to PEO (Li+ > Na+ > K+ > Cs+).66−69 The obtained trend was attributed to a reduction in charge density in the listed order; the dominant effect of solvation in liquid phase was thoroughly discussed.70 Li+ also binds to PEO in acetonitrile, also underlining the importance of the solvent.16,17 The results can be compared to those obtained with 18crown-6-ether, a cyclic analogue of PEO. For monovalent cations, the overall trend in both water and methanol is roughly the same as the one obtained here. Concerning the divalent cations in water, no association was observed for Ca2+, whereas Pb2+ and Ba2+ showed the strongest binding.71 This has been ascribed to the strong hydration and small size of Ca2+ and to the adequate ionic radius of Ba2+ as well as its high charge in the absence of strong hydration effects.72 In methanol, the same trends as in water were obtained for the divalent cations. However, as interactions are enhanced in methanol, Ca2+ had a significant binding constant in methanol.73 It can be speculated that the much higher association of cations with 18-crown-6 is, in part, due to the so-called “macrocyclic effect”,72 where the crown ether is already preorganized so that several oxygens can interact with the cation without the entropy cost such an arrangement would impose in a free PEO chain. Considering the organization of the PEO chain upon cation binding, one can consider the differences between the selfdiffusion coefficient values of PEO observed in the different salt solutions (see the SI). Whereas DPEO in general changes only by an amount that is comparable to experimental error, at csalt = 2 mM, the average DPEO value for strongly binding ions (K+, Rb+, Cs+, and Ba2+, ca. 7.9 × 10−11 m2 s−1) is significantly smaller than the same average for nonbinding ions (ca. 8.5 ×

Table 2. Ionic Radii, Surface Charge Densities, Hydration Numbers, and Solvation Numbers of Cations

cation

ionic radius rion (Å)a

surface charge density σ/e (Å−2)b

nStokesc

nModeld

ADHN

Li+ Na+

0.69 1.02

0.17 0.08

7.4 6.5

5.2 3.5

0.58 0.22

K+ Rb+ Cs+ Mg2+

1.38 1.49 1.70 0.72

0.04 0.04 0.03 0.31

5.1 4.7 4.3 11.7

2.6 2.4 2.1 10.0

Zn2+

0.75

0.28

11.3

9.6

2.18

Cd2+ Ca2+

0.95 1.00

0.18 0.16

11.4 10.4

7.6 7.2

2.09

Ba2+

1.36

0.09

9.6

5.3

0.35

Al3+ Sc3+

0.53 0.75

0.85 0.42

16.8

20.4 14.4

8.68

0

5.73

e

solvation numbers in MeOHf 12.4 11.2 (3.4) (3.8) 8.6 7.3 6.2 (14.0) (11.1) 31.2 (14.3) (11.3) 29.1 (12.0) (9.4) 25 (10.3) (8.5)

a From Marcus.74 bCalculated on the basis of ionic radii from Marcus.74 cnStokes, hydration number derived from Stokes radii.74 d nModel, hydration number derived by from Gibbs free energy and enthalpy of hydration.74 eADHN, apparent dynamic hydration number derived from size exclusion chromatography experiments.75 fSolvation numbers obtained from entropies of solvation,76 and from volumes and compressibilities for ions in methanol,77,78 respectively, in parentheses.

radii, the binding of the monovalent cations to PEO chains seems to be size-related, with stronger binding for larger ions, as that for the crown ethers in methanol and water solutions.71,73 Also Ba2+, the largest of the multivalent cations examined here, binds relatively strongly. But if binding was exclusively size-dependent, Ca2+ and Cd2+, which have radii close to that of Na+ (r = 1.00 and 0.95 Å, respectively, 10363


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exact opposite to that observed in the gas phase. The relative magnitudes of binding among the ions with charge densities below 0.1 Å−2 are however not well correlated with the surface charge density. Although it is primarily the cation that associate with PEO, for Ba2+, the anion also associates with the polymer− cation complex, probably in the form of ion pairs.

compared to 1.02 Å) should also bind. Clearly, size alone does not steer binding. In addition, our observed trend does not follow the typically assumed Hofmeister sequence, well in accordance with conclusions in a recent compilation3 of specific ion effects in nonaqueous solvents. Characterizing the strength of electrostatic interaction at the ion surface, the surface charge density (or, after rescaling, the electric field strength at the ion surface) of the cations

σ=

■

S Supporting Information *

zcation 2 4πrion

ASSOCIATED CONTENT

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcb.6b08923. Raw electrophoretic mobility and self-diffusion coefficient data, equilibrium binding constants, the effect of small amount of added water, screening lengths, and fitting parameters (PDF)

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can be explored. This property has, indeed, been implicated in noncovalent association of ions79 and is the governing parameter within the “lyotropic series”.3,80 From the known ionic radii rion and the nominal charges zcation, σ can be readily calculated (Table 2). As can be seen in Figure 3, there seems to be a sharp threshold in surface charge density around 0.10− 0.15 Å−2 that separates weak and strong binding. Contrary to what might be expected, the cations with charge density below this threshold show a stronger binding. We propose that the explanation for this is that high charge density cations bind solvent molecules more strongly (see trends in Table 2). This would prevent them from binding, in competition with the solvent, to the PEO moiety. It has been suggested previously that cation binding to PEO can be counteracted by strong solvent−cation22 or solvent−polymer interactions.17 It is interesting to note that surface charge density has thereby an opposite effect in the liquid and gaseous phases.70 Although hydration of cations in water was extensively probed in the past, unequivocal and quantitatively meaningful hydration numbers are not straightforward to define, and those hydration numbers differ a lot depending on the way they have been obtained (Table 2). Unfortunately, cationic solvation in nonaqueous solution is less explored and for methanol, reported solvation numbers76−78 seem to scatter even more than hydration numbers. Because of this and the fact that the list of solvation numbers reported in methanol is incomplete, the discussion below will also be based on hydration numbers. A comparison of hydration and solvation numbers74−76 reveals that the polyvalent cations are generally more hydrated/ solvated than the monovalent ones. Yet, the apparent dynamic hydration number75 of Ba2+ is considerably smaller than that for the other polyvalent ions examined.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel: +46 87908592. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Support from the Swedish Research Council (VR) is gratefully acknowledged. REFERENCES

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CONCLUSIONS We demonstrate that the combination of electrophoretic and diffusion NMR experiments is capable of characterizing quantitatively the binding of a large variety of ions to uncharged polymers. For monovalent ions, the obtained effective charges, with magnitude up to ca. 0.01 elementary charge per monomer, provide an accurate measure of the number of cations bound to the investigated PEO polymer. The experiments were performed at a low polymer concentration and at sufficiently low ionic strength so that ion−ion interactions do not significantly modify the observed trends over the entire range of investigated ions. Our results indicate that binding of cations to PEO in methanol correlates strongly with the cation surface charge density: the binding is clearly stronger below 0.10−0.15 Å−2 than that above this range. The explanation proposed is that cations with high surface charge density bind solvent molecules harder, reducing ionic interaction with the polymer, a trend 10364


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Binding of Monovalent and Multivalent Metal Cations to

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