Complexing Cations by Poly(ethylene oxide): Binding Site and

Article pubs.acs.org/JPCB

Complexing Cations by Poly(ethylene oxide): Binding Site and Binding Mode Yuan Fang, Marianne Giesecke, and István Furó* Division of Applied Physical Chemistry, Department of Chemistry, KTH Royal Institute of Technology, SE-10044 Stockholm, Sweden S Supporting Information *

ABSTRACT: The binding of K+ and Ba2+ cations to short poly(ethylene oxide) (PEO) chains with ca. 4−25 monomeric units in methanol was studied by determining the effective charge of the polymer through a combination of electrophoretic NMR and diffusion NMR experiments. These cations were previously found to bind to long PEO chains in a similar strong manner. In addition, 1H chemical shift and longitudinal spin relaxation rate changes upon binding were quantified. For both systems, binding was stronger for the short chains than that for the longer chains, which is attributed mainly to interactions between bound ions. For K+ ions, the equilibrium binding constant of a cation to a binding site was measured. For both cations, the binding site was estimated to consist of ca. six monomeric units that coordinated with the respective ions. For the systems with barium, a significant fraction of the bound ions are (BaAnion)+ ion pairs. This leads to a strong anion effect in the effective charge of the oligomers acquired upon barium ion binding. For K+, the coordinating oligomer segment remains rather mobile and individual oligomers exchange rapidly (≪s) between their free and ion-complexing states. In contrast, segmental dynamics slows significantly for the oligomer section that coordinates with the barium species, and for individual oligomers, binding and nonbinding sections do not exchange on the time scale of seconds. Hence, oligomers also exchange slowly (>s) between their free and barium complexing states.

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INTRODUCTION Ion binding to polymers and the changes induced thereupon in molecular and material properties constitute an active area of research within physical chemistry. In particular, the relation between the various ions, both anions and cations, as concerning the binding strength or nature of changes induced by binding poses many questions. Frequently, the empirical sequence of ion-induced effects follows a particular order. Often, this order1−4 complies with the so-called Hofmeister series,5 whereas in other situations it is the so-called lyotropic series6 that seems to be relevant; observations depend on materials, solvents,7 and phenomena. Unraveling the molecular mechanism behind those series, both anionic and cationic, inspired a lot of investigations.1−4 One particular subgroup of those concerns ion-binding to noncharged synthetic polymers. Studying this question is important not only because such polymers can constitute useful model systems but also because they have applications8−12 where ions and their binding influence the properties of interest. In a previous study,13 we have examined the association of cations in methanol with a neutral polymer, poly(ethylene oxide) (PEO) with a combination of electrophoretic NMR (eNMR) and diffusion NMR methods. Methanol, a solvent used in numerous previous studies, was selected because PEO exhibits strong binding of cations in it. Those cations are © XXXX American Chemical Society

supposed to bind by having coordinated with the negative charge density localized on the ether oxygens. For a large set of mono- and multi-valent cations and a PEO chain having a length of ca. 500 monomers, we obtained the effective charge of the polymer that is attained by having associated cations and showed that binding occurs below a certain critical surface charge density of the ions. This finding suggested a universal behavior and thereby we have set out to investigate if the binding of two of the strongest binding ions,13,14 monovalent K+ and divalent Ba2+ were, indeed, similar in molecular details or not. Besides characterizing the cation binding via the effective charge, we have also studied the NMR spectral features appearing upon ion binding and complemented those with NMR relaxation data. To reveal new information, we have selected to study a diverse group of short PEO chains with different chain lengths and different end groups. For reference, we have also investigated the binding of Li+ that was previously shown to be negligible for longer PEO chains.13 Short chains were previously indicated14−27 to exhibit a binding that was stronger than that for longer chains (crown ethers, i.e., cyclic short PEO Received: December 8, 2016 Revised: February 14, 2017 Published: February 15, 2017 A

DOI: 10.1021/acs.jpcb.6b12381 J. Phys. Chem. B XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry B Table 1. Properties of the Studied Polymers name of compound a

P194-OH P360-OHa P660-OHa P1210-OHa P347-OMeb P1199-OMeb P22000-OHd

number-average molecular weight Mn

weight-average molecular weight Mw

PDI = Mw/Mn

averagec number of monomers Np

194 300 600 1100 310 1100 20 000

196 360 660 1210 347 1200 22 000

1.01 1.2 1.1 1.1 1.12 1.09 1.1

4.0 6.4 13.2 25 6.0 24 450

Alcohol end group. bMethoxy end group. cFrom the number-average molecular weight. The total mass also includes the chain ends (H and  OH or, in the methylated case, CH3 and OCH3). dUsed in our previous study.13

a

coefficients of the oligomers were obtained by fitting the conventional Stejskal−Tanner expression

chains, exhibit even stronger binding28,29). Yet, high-quality quantitative data are still lacking with regard to the variation of binding over the chain length. The latter feature is important in two respects. First, it is unclear what is the structural motif or, in an alternative formulation, the size of the ion binding site in a PEO chain. This is also a question of practical importance as coordination is one of the most important factors that determine the ionic conductance in solid (amorphous) polymer electrolytes, such as neat PEO.30−33 Second, ion binding to long polymer chains is strongly influenced by ion−ion interactions.34−39 For shorter pieces of the polymer chain to which only single ions can bind and at low polymer and salt concentrations, ion−ion interactions have no effect. Hence, the binding behavior of short polymer chains can be compared to observations in longer chains. Interpreted within the framework of particular models,34−39 this can also be used as a test of available theories. How anions affect the binding of cations was also investigated because anions show nontrivial specific effects and, moreover, in polymer electrolytes they influence ion conduction.31,33,40

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

(1)

to the variation of the NMR spectral integral of PEO acquired, where S and S0 are the integral intensities with and without a gradient, respectively, and γ is the magnetogyric ratio.42 The gradient strength was calibrated using the known value of trace 1 H diffusion coefficient in heavy water.43 In eNMR experiments, a double-stimulated echo pulse sequence with bipolar electrophoretic voltages was used.44 The experimental instrumentation, including the eNMR sample cell and procedure, has been described previously in great detail.13,45 The electrode−electrode distance was approximately 31.2 mm (as calibrated by eNMR experiments in a 10 mM tetramethylammonium bromide45 solution in D2O). The electric field E was stepped up from 0 to a maximum of ± 128 V cm−1 in at least 10 steps, whereas all other parameters were kept constant. The duration δ and amplitude g of the gradient pulses were 1 ms and 18.6 G cm−1, respectively, whereas the drift time, ΔE, was set to 200 ms. The previously described reference phase correction method13,45 was used to obtain the electrophoretic mobilities μ of the PEO units without bulk flow artifacts caused by thermal convection and/ or electro-osmosis. A slight temperature increase due to Joule heating in the eNMR experiments was corrected for, as previously,13 by exploiting the known temperature dependence of methanol viscosity.46 The electrophoretic mobilities, summarized in the Supporting Information (SI), together with the self-diffusion coefficients, were obtained by fitting a straight line to the electrophoretic modulation

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EXPERIMENTAL SECTION PEO samples of short length and of low polydispersity index (PDI) were purchased from Polymer Source Inc and used as received. The properties of the studied molecules are summarized in Table 1 together with the names they are cited by. Metal (Li+, K+, Ba2+) acetate (purity ≥99%) and perchlorate (purity ≥99%) salts and methanol-d4 (nominal 99.8% D) were purchased from Sigma-Aldrich. Samples probed contained PEO at cPEO = 2 mM monomeric concentration and metal acetate (or perchlorate) salt at csalt = 2 mM (or at some selected other concentrations) in methanol-d4. The water concentration in each sample was in the order of 20 mM. Previous studies13,25 showed that having water in methanol up to 0.1 v/v had no significant effect upon ion binding. All 1H NMR experiments were performed at 298 K on a Bruker Avance 500 spectrometer, equipped with a conventional 5 mm high-resolution probe with a gradient coil capable of supplying 50 G cm−1 maximum gradient strength in the z direction. The longitudinal relaxation rate, R1 (the inverse of the relaxation time, T1), was measured by conventional inversion recovery; all communicated results were derived from decays that appeared as single exponential and thereby fitted with single-exponential functions. The diffusion experiments were performed using a double-stimulated echo pulse sequence.41 The duration of the gradient pulses, δ, and the total diffusion time, Δ, were set to 3 and 400 ms, respectively. The amplitude, g, of the pulsed field gradients was stepped up linearly from 0.95 to 17.7 G cm−1 in 16 steps. The diffusion

ϕ = γgδ ΔEμE

(2)

of the NMR signal phase difference, ϕ, between the PEO and methanol methyl peaks. Those peaks are shown in the illustrative 1H NMR spectrum in Figure 1. Representative spectral series, with the phase modulation effects visualized, are presented in the SI (Figure S3). The diffusion coefficient and the electrophoretic mobility were used, through the Nernst−Einstein relation,47−49 to express the effective charge zPEO (in units of elementary charge) attained by the oligomers by association with cations z PEO =

kBT μ e D

(3)

where kB represents the Boltzmann factor, T is the absolute temperature, and e is the elementary charge. B


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The Journal of Physical Chemistry B

Figure 2. Change of the average 1H chemical shift of the in-chain PEO moieties (see Figure 3) upon addition of salts with K+ (squares) and Ba2+ (circles, acetate anions; triangles, perchlorate anions) cations, for oligomers with hydroxyl (solid symbols) and methyl (open symbols) end groups. The situations where the PEO peak was split (see Figure 3 and text) are indicated by magenta symbols. The shift values for K+ are also tabulated in the SI for quantitative analysis. The connection between the molecular weight and size in terms of the average number of monomers is given in Table 1. The errors are presented in the SI; for data with no explicit error bars, the error is below symbol size.

Figure 1. 1H NMR spectrum of P1210-OH at 2 mM monomeric concentration in methanol-d4. The peak at 3.4 ppm corresponds to methanol methyl protons, the one at 3.7 ppm corresponds to ethylene oxide protons in PEO, and the peak at 4.9 ppm arises from exchangeable protons in HDO and the OH groups in methanol and PEO. The asterisk marks the signal from the ethylene oxide groups at the chain ends. In eNMR experiments, the PEO peak(s) become phase modulated relative to the methanol and water peaks.

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RESULTS AND DISCUSSION Spectral Effects of Ion Binding. The 1H NMR spectrum of all PEO solutions contained, without added salt, one major signal that corresponds to the oxyethylene protons, as shown in Figure 1. In addition, the oxyethylene group closest to a chain end contributes to the spectrum at a slightly lower chemical shift, irrespective of whether the chain end is an OH or an  OMe group. In addition, the end methyl in the methoxyterminated molecules provided a signal that overlapped with the methanol peak; this contribution is K+ > Li+, with Li+ ions showing no significant binding, in agreement with earlier studies.16,17 The effective charge of PEO with K+ increases with molecular weight of the PEO polymers. Similar effects have been observed18,19 for the binding of both K+ and Na+. For Ba2+, the effective charge presents a different trend that, together with the spectral differences (see Figures 1−3), suggests that K+ and Ba2+ could differ in their binding mechanisms. We shall further analyze this point in what follows. With regard to ion binding, there are two effects to consider. First, the binding of ions to neutral polymers is affected by ion−ion interactions.34−39 In long PEO chains, this effect may be considered within the framework of suitable theories, and extrapolation of the observed binding trend to zero ion concentration may yield the equilibrium binding constant K0, characteristic of the binding in the absence of interactions among the bound ions.13 With one particular theory,34,35 we previously obtained K0 = 390 for K+. In short PEO chains, there may not be place for multiple ions to bind (actually, this statement requires information about the size of the binding

In this expression, Nb is the size of the binding site in terms of number of monomers coordinating with the cation, whereas the concentration of the bound ions is simply obtained as cbound = nboundcoligomer, where coligomer = cPEO/Np (recall that cPEO = 2 mM is the concentration on a monomeric basis, and see Np in Table 1) and nbound is the number of the bound ions per oligomer. If we assume that our investigated oligomer in Figure 5 with Np = 6 can only bind a single ion (that is, assuming Nb = 6), the above expression simplifies to nbound 1 K0 = (1 − nbound) (csalt − nboundcoligomer) (6) The parameter nbound can, as has been done previously for long PEO chains,13 be estimated from the effective charge as z nbound = PEO Zcation (7) where Zcation is the nominal cation charge (=1 for K+). However, ion−ion interactions in the solution affect ionic mobilities.51 For that reason, the effective charges obtained via D


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zPEO (recall eq 9), this indicates having nbound > 1 for a significant fraction of oligomers. The situation is a bit more complex for the systems with Ba salts. On one hand, Ba2+ is a divalent ion. Hence, ion−ion interactions would restrict binding of two Ba2+ ions to any of the investigated oligomers. However, in contrast to monovalent ions, Ba2+ exhibits significant pairing with anions, both in bulk and while binding to PEO.13 In the latter case, (BaAc)+ ion pairs were shown to have some association. Ion pairing depends on the involved ion type (in a complex manner − recommended ionic radii of perchlorate and acetate ions are very close, 0.24 and 0.23 nm, respectively61), and therefore, it can be qualitatively assessed by investigating the dependence of cation binding on the anion. Such data are presented in Figure 6 with perchlorate and acetate salts. Clearly, with acetate, we

eq 3 deviate from the actual nominal charges of the investigated ionic species, in our current case, the PEO oligomers with bound cations. This is particularly the case for nonaqueous solvents52 with low dielectric constants, whereas in aqueous solutions,53 this effect is very small for monovalent ions. For the system investigated here with small oligomers and monovalent ions and at the explored low ionic strength,54 the effect of the (counter)ion atmosphere can be well approximated by the Onsager limiting laws.55,56 As has been shown previously,52 in that regime and for anions and cations of similar self-diffusion coefficients (recall that the self-diffusion coefficient of the perchlorate anion is57 ca. 1.8 × 10−9 m2/s, whereas the selfdiffusion coefficient of the cation-binding oligomer (see Table S1 in SI) is ca. 0.7 × 10−9 m2/s), the simple relation zeffective = 1 − κR h znominal (8) can be derived between the effective and nominal charges, where κ is the reciprocal Debye length. Using this approximation and the hydrodynamic radius as obtained from a simple spherical model, we can estimate the average nominal charge of the PEO oligomers from the measured effective charges as z PEO nbound = (1 − κR h)Zcation (9) Hence, the effective charge values shift up slightly with an amount that increases with increasing ionic strength. With full expression of the limiting law52 (that is, using the explicit values of the oligomer and anion self-diffusion coefficients), one obtains the corrected data points in Figure 5 (within error, coincide with values derived by the simplified expression in eq 9), and the obtained binding constant becomes K0 = 560 ± 60, which compares favorably to K0 = 390 obtained in the more complex situation of multiple cations bound to much longer PEO chains.13 The obtained binding constant K0 ≈ 500 provides that the free energy of binding at a binding site kT ln K0 is ca. 6kT. This value is for K+. Yet, considering that barium binding was in many respects similar to potassium binding (with K0 being estimated to be ca. 40% lower in a long-chain PEO13), 6kT is a good estimate for the free energy of binding of Ba ionic species as well. The minimum requirement for binding of two ions is that the electrostatic repulsion between those ions is smaller than the free energy of binding. The electrostatic term depends on the available ion−ion distance. Evaluating our diffusion data (see SI) in terms of a rodlike polymer model58,59 sets the maximum ion−ion separation to 3.3 nm with Np = 24−25 and to 1.2 nm with Np = 13.2. Recall in addition that the bound ions are buried by the PEO environment, where the dielectric constant is ca. 10.31,60 Thus, the Bjerrum length can be approximated to 6 nm. Hence, our largest oligomers with Np = 24−25 are permitted to bind two monovalent cations (with an approximate energy cost of 2kT) or one divalent and one monovalent cation (4kT). By the same argument, the Np = 13.2 oligomers should dominantly bind only single cations. Although our simple argument does not account for the loss of conformational entropy for the chain between the ions, some of these conclusions are supported by the data in Figure 4. Namely, for the oligomer with Np = 24 (P1199-OMe) in our 2 mM equimolar mixture with KAc, we obtain the effective charge of zPEO = 0.98. Because at those concentrations the binding sites cannot be saturated (recall Figure 5) and nbound >

Figure 6. Effective charge zPEO as estimated by eNMR and diffusion NMR experiments (see eq 3) at 2 mM monomeric concentration of polymer and 2 mM acetate and perchlorate salts in methanol-d4.

obtain smaller positive charges and thereby acetate anions in the form of (BaAc)+ seem to associate with the PEO chain more than the perchlorate anions do. We stress that the effective charge remains positive, and therefore, the association of the cations dominates. For the oligomer with Np = 25 (P1210-OH) and Ba(ClO4)2 as the salt, we obtain the effective charge of zPEO = 2.1. As this cannot be achieved by binding of Ba(ClO4)+ cations, there is a clear case for mixed association of both Ba2+ and Ba(Anion)+ cations with our longest PEO oligomers. For the oligomer with Np = 6.2 (P360-OH), the effective charge with perchlorate is zPEO = 1.6 even though this oligomer cannot bind multiple ions which shows that in the smallest oligomers, the binding of Ba2+ must dominate. Yet, the diffusion of the acetate anion is different with and without P360-OH present (respectively, D = 8.8 × 10−10 and 9.7 × 10−10 m2/s) and zPEO is lower (but still >1) with acetate than with perchlorate: hence, (BaAc)+ seems to bind to some extent even to the smallest oligomers. This finding (dominant divalent binding at small oligomers, mixed divalent/monovalent binding at larger oligomers) is simply a consequence of ion−ion interactions influencing the behavior of the larger oligomers: the electrostatic cost of having two divalent ions is very large. The acetate and perchlorate anions seem to have similar ionic radii61 and solvation (in water, no sufficient data exist for methanol) numbers.61 As to why the acetate anion would bind more to the polymer−cation complex is unclear and requires further investigation. In general, information on anion E


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K+. This again points to the role of the chain entropy loss. Because the enthalpy gain is higher for the double-charged Ba2+, Ba2+ binds to P194-OH. From the NMR spectrum in Figure 3, it is clear that all five ether oxygens participate in coordinating with Ba2+, which is not the case for the larger oligomers (see more about this below). Yet, Ba2+ binds strongly to slightly larger oligomers and above Np ≈ 6, barium ion binding in whatever form is about as strong as possible, whereas potassium binding above Np ≈ 6 is significant, as it shows only minor increase upon increasing Np from ca. 6 to ca. 13. In summary, the binding motif of an open PEO chain seems to contain a bit less than six monomer units for barium and a bit more than that in potassium, which is well in line with the high affinity of 18-crown-6 for either of these ions.27,28,65 Hence, calculating the binding constant, as in Figure 5, is well justified. Particularly for K+, the number of coordinating EO units has been discussed,15,16,18,23 though usually on the basis of less experimental evidence, and suggestions lie around 6−7 units. In other cases, it was proposed to be much less17 (approximately 4) or much more73 (ca. 10). Regarding the effect of methoxy end groups, although the addition of CH3 changes the electric charge on the neighboring oxygen (recall the similar substituent constants74 for H and CH3) only slightly, it adds steric hindrance. For barium, this suppresses binding, whereas for potassium it does not. Significant end-group effects were also observed by others14 for short PEO chains with 5 units, specifically a lower affinity for Ba2+ with methoxy end groups (whereas the difference for K+ was small). This seems to indicate that there are differences in chain conformations around those two ions. It has been suggested23 that end groups are not coordinating with the cation for K+; indeed, this seems to be consistent with our data (that is, the lack of end-group effects). Regarding the relation of our data to previous literature findings, the binding constant as obtained via eq 6 in Figure 5 is suitable when it comes to characterizing the free energy of binding of ions to a binding site. Yet, binding constants available in the literature were often calculated on the basis of eq 4 with [P] simply set to the polymer concentration (or, sometimes, monomer concentration). Re-calculating our data under the same terms permits us to state that, for oligomers, our binding trends are well in line with the somewhat scattered literature record (see Figure S1). As has been discussed in detail,14,25,65,66,75 the binding constants for the short-chain PEO obtained here are several orders of magnitude lower than that for their cyclic analogues (crown ethers) with the same number of EO units in methanol. This “macrocyclic effect”,76 already mentioned above, was thoroughly analyzed in enthalpic and entropic terms.14,24,25 State of the Polymer upon Cation Binding. In addition to the spectral features in Figure 3 and the observed effective charges in Figure 4, we also interpret the observed PEO 1H longitudinal relaxation rates collected in Figure 8. Changes in these relaxation rates report about changes in molecular dynamics of the CH2 groups within the oligomers. 1H longitudinal relaxation in PEO reports about the fast segmental dynamics within the very flexible chains.77 This is also verified by the observation that the relaxation rates in salt-free state are very similar for the oligomers of different size (see Figure 8). In the model we develop here, we shall rely heavily on the observation that the different oxyethylene peak components within the same spectrum recorded for systems with added Ba salt in Figure 3 have shown the same behavior in electrophoretic

association with PEO is scarce, yet failing to account for the association of the anions was found to give significant differences in assessing binding.62,63 Regardless of anion pairing, ion−ion interactions and chain entropy effects limit binding upon increasing polymer size. This is illustrated in a qualitative manner in Figure 7.

Figure 7. Effective charge per monomer and its variation with polymer length with KAc (black square) and Ba(Ac)2 (red circle) salts (data from from Figure 5 and previously obtained results for P22000-OH13).

Assessing the Binding Site. Crown ethers, the cyclic EO oligomers, form a useful starting point for this discussion. Their affinity to various metal ions depends on the macrocyclic ring size. 9-Crown-3 is known64 to bind only the smallest alkali ion, Li+, whereas both K+ and Ba2+ (or, (BaAnion)+) have the largest affinity to 18-crown-6.27,28,65 For noncyclic polyethers, there is no preorganized ring, but the polyether chain is flexible and could adjust its conformation so that the local dipole moments of the oxygens are directed toward the cation.24 Hence, the binding site is plausibly a chain section wrapped around the metal ion in a quasicyclic (helical) structure.23,25,66−69 This picture is consistent with helical features observed in neat solid state or melt.70,71 A recent study has indicated that PEO in methanol mostly adopts a random coil configuration but may assume a helical conformation locally.72 Below we specifically address the information provided by our data in Figures 2 and 4 about the length of the chain section that ions favor to be coordinated with. Clearly, the size is slightly ion dependent. First of all, Li+ does not bind to any of the oligomers here, even though it binds to 9-crown-3.64 Hence, one can conclude that loss of chain entropy associated with making such a tight loop is significant in relation to the other components in the free energy, namely, the binding enthalpy14,24,25 and the gain of entropy associated with the release of the solvent14 coordinating with the Li+ ion in bulk. The larger K+ and Ba2+ (or, (BaAnion)+) ions require larger coordinating sections with smaller curvature and smaller corresponding loss of chain entropy. Even though K+ and Ba2+ ions have very close radii (0.138 and 0.136 nm, respectively), they clearly do not exhibit the same behavior − this difference is thereby not a size effect but connected to the larger surface charge density for Ba2+. K+ clearly does not bind to our shortest oligomer P194-OH with Np = 4, whereas 15crown-5 with the same number of ether oxygens strongly binds F


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between the free and cation-binding states, as in Figure 2, expressed in Hz78) of this shortest oligomer between free and cation-binding states. As we have established earlier, the binding motif of the oligomer chain that binds the barium species is ca. 6 monomers long. P194-OH, being shorter than that, binds some cations but weakly enough to permit their fast exchange. In contrast to the samples with barium, with K+ ions, we have single and narrow PEO peaks everywhere, and thereby, we do not see any trace of long-lifetime states. Hence, segments within oligomers exchange rapidly between K+-coordinating and noncoordinating states, whereas whole oligomers exchange rapidly between K+-binding and free states. We note in this context that previous investigators20,21 inferred from the same type of observation (single and narrow PEO peaks in dichloromethane with potassium salts added) that all oxygen atoms must participate evenly in the complex formation, in the same way as in a crown ether. Fast exchange furnishes another and simpler explanation for that observation. In the dynamic regime of fast (with correlation times below the inverse NMR frequency78) molecular motions, which is the case for PEO chains,77 the relaxation rate increases with increasing motional correlation time. Hence, the data in Figure 8 report that, in general, segmental motions in our PEO oligomers become slower upon ion binding. Similar findings at much higher K+ concentrations have been reported previously.15 In line with our discussion in the previous section, this effect is quite different for bound potassium and barium ions, with barium ions having a much larger immobilizing influence on the oligomer segments. As concerning the systems P1199-OMe and P1210-OH with barium, Figure 8 confirms (by having R1 values for both signal components much higher than that for the respective free oligomers) that, for those systems, there are virtually no oligomers without binding some barium species. The data also strengthen our previous observations regarding binding and nonbinding segments within the same oligomer: for the signal at larger chemical shift (denoted Ba-2 in Figure 8) and thereby more directly involved in binding, we obtain slower segmental dynamics signified by higher R1. Yet, even those parts of the chain that do not coordinate with the barium cations experience, on average, slower segmental motions, which probably reflects the orientational degrees of freedom being limited by neighboring segments being fixed in position by the cation. We finally note that the conformation, as reflected by the hydrodynamic radius and thereby the obtained diffusion coefficients, D (see Figure S2), has one general trend, that is, D remains constant or slightly increases (the hydrodynamic radius decreases) with K+, whereas D slightly decreases (and the hydrodynamic radius increases) with Ba ions. This seems to suggest, in line with the discussion above, that upon coordinating K+ cations the oligomer chain remains flexible and can attain a close-to globular conformation. In the case of barium, chain segments pointing outward from a rigid coordinating core increase the hydrodynamic radius.

Figure 8. Longitudinal relaxation rate R1 of the 1H PEO signal recorded at 2 mM monomeric concentration of polymer and 2 mM salt concentration in methanol-d4. For samples P1199-OMe and P1210-OH, the PEO spectrum is clearly split, and Ba-1 denotes the component at lower chemical shift and Ba-2 the component at higher chemical shift (see Figure 3).

and dif f usion experiments. In contrast, in those two cases (P1199-OMe and P1210-OH, uppermost spectra in Figure 3), where the split lines were well separable, the obtained R1 values were dif ferent for the different spectral components. Hence, for those samples we present two relaxation rates in Figure 8. Regarding first the split spectra in Figure 3 for P1199-OMe and P1210-OH with Ba2+ present, the different spectral components exhibit identical self-diffusion coefficients and electrophoretic mobilities, both derived from micrometer-scale displacements but different longitudinal relaxation rates that are defined by local molecular motions. Hence, the inescapable conclusion is that those spectral components arise from dif ferent regions of the same polymer chain. We identify those regions with parts of the chain that are directly involved and not directly involved in coordinating with the associated metal ions. In addition, different R1 values were obtained for the different spectral components. Because the experimental time scale in the inversion recovery experiments was in the order of 1/R1 ≈ 1 s, we must also accept that the lifetime of polymer states that bind Ba2+ or (BaAc)+ or, possibly, BaAc2 is long on the time scale of 1 s. Furthermore, we note that at the studied concentrations, we observed no PEO peak at its original (that is, without added BaAc2) chemical shift in the P1199-OMe and P1210-OH samples. Hence, we must also conclude that in those solutions practically all oligomer chains bind a Bacontaining species. In connection to this, the eNMR and diffusion NMR experiments monitor only the population averages of the electrophoretic mobility and self-diffusion coefficient, respectively. Hence, our effective charges are population averages over PEO molecules that bind Ba2+ or (BaAc)+ or a combination thereof, even in the case of slow exchange. In contrast to the longer oligomers, the spectra of P347-OMe and P360-OH with barium acetate exhibit significant spectral intensity at the chemical shift of native in-chain PEO groups, signifying the presence of the native (with no bound cations) oligomers. Finally, the spectrum PEO-194-OH contains a single EO peak but at the chemical shift (see Figure 2) that seems to be between those characterizing free and cation-binding states. Hence, there is a fast exchange (exchange times short as compared to the inverse of the chemical shift difference

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CONCLUSIONS We have investigated here how K+ and Ba2+ ions interact in methanol with PEO chains of various chain length and chain ending. One main question posed was whether the molecular features for the binding of those two ions to PEO are the same or not. The motivation for this question arose from our previous study,13 where we detected that only cations with a G


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The Journal of Physical Chemistry B surface charge density below a certain threshold bind to longchain PEO. Both K+ and Ba2+ ions exhibit surface charge densities below the threshold and they have shown similarly strong binding. The other main question was to provide more certainty regarding the binding site, its size, and molecular structure. Regarding this, conclusions from previous studies were scattered and partly contradicting to each other. The results were obtained with PEO oligomers of 4−25 monomeric units with potassium and barium salts, with either acetate or perchlorate as anions. Both polymer and salt concentrations were low, at most several mM. In a short (ca. 6 monomers long) oligomer, we estimated binding as it depends on the salt concentration from effective charges, derived in turn from diffusion NMR and eNMR data. After having accounted for the effects of ion−ion interactions in solution, we derived from the data the equilibrium binding constant that also provided us with an estimate of the free energy of binding to the binding motif of the PEO chain. From that one could predict that the largest oligomers investigated here bind multiple cations, a finding that was verified by the data for those latter oligomers. Hence, the finding of cation binding being stronger to shorter chains as compared to that to longer chains14,27 is shown to be strongly related through ion−ion interactions between bound ions. In systems with barium salts, small oligomers dominantly bind Ba2+ ions, whereas in larger oligomers at least one of the bound ions can be a (BaAnion)+ ion pair. The NMR spectra and chemical shifts derived from them and the effective charges and the variation of these features over the oligomer size range suggested that the size of the binding motif was approximately six monomer units, with both potassium and barium salts. This is roughly the middle of the range suggested by previous scattered literature findings. Yet, our data have been achieved by the same methodology applied to a broad range of oligomers. Yet, the same data together with longitudinal spin relaxation rates also suggest that the polymer structure and dynamics are both quite different for the two different metal ions. First of all, upon complexing metal ions, the segmental dynamics of the ethylene oxide units slows down. This is a rather small effect for K+ ions for which we could also show that (i) oligomers are in fast exchange between complexing and noncomplexing chains and (ii) individual segments within the same oligomer are also in fast exchange between coordinating and noncoordinating position in relation to the metal ion. Hence, with K+ as the bound ion, the oligomers are highly dynamic. With bound Ba2+ and/or (BaAnion)+ cations, segmental motions slow down substantially. With the exception of the shortest oligomer with just four monomers, the barium-containing complexes also exhibited long lifetimes. In addition, the oligomers did not freely re-arrange themselves in the complex; on the time scale of seconds, particular monomers within the binding motif remain in a dynamically hindered coordinating position in relation to the metal ion, whereas the segments outside the binding site remain noncoordinating. Hence, in the latter respects, Ba2+ and K+ cations behave quite differently. All of these features are interesting subjects to molecular modeling approaches.

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Raw data used for calculating the effective charges: the self-diffusion coefficients and the electrophoretic mobilities for PEO in the studied samples; the spectral shift experienced by the PEO signal upon addition of K+ and Ba2+; the binding constants of K+ and Ba2+ cations obtained in this work and from the literature; the diffusion coefficients of PEO molecules at 2 mM monomeric concentration of polymer and 2 mM salt concentration in methanol-d4; the variation of the 1H spectral shape with increasing electric field strength (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

István Furó: 0000-0002-0231-3970 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Support from the Swedish Research Council (VR) is gratefully acknowledged. Y.F. acknowledges the China Scholarship Council (CSC) for doctoral fellowship support.

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REFERENCES

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcb.6b12381. H


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Complexing Cations by Poly(ethylene oxide): Binding Site and

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