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Mobility of Cations and Water Molecules in Sulfocation-Exchange Membranes Based on Polyethylene and Sulfonated Grafted Polystyrene

Abstract

The main patterns of the hydration of sulfo groups, the translational mobility of water molecules, alkali metal cations, and ionic conductivity in sulfocation-exchange membranes (MSC) based on polyethylene and sulfonated grafted polystyrene have been investigated using NMR and impedance spectroscopy techniques. It has been shown that at moisture contents λ < 4 (λ is the number of water molecules per sulfo group) the H+ counterions in the membranes form diaquahydrogen ions \({{{\text{H}}}_{{\text{5}}}}{\text{O}}_{{\text{2}}}^{ + }{\text{.}}\) In the temperature range below 0°C at λ < 12, water molecules retain high mobility and do not form the ice phase. Water molecules diffusion coefficients (for the H+ form, the average diffusion coefficient of water molecules and acidic protons) and first for ion-exchange systems, and the diffusion coefficients of counterions Li+, Na+, and Cs+ have been measured by pulsed field gradient 1H, 7Li, 23Na, and 133Cs NMR spectroscopy. In MSC membranes in contact with water, the self-diffusion coefficients of cations increase in the Li+ < Na+ < Cs+ series. The cation conductivity values are in the same Li+ < Na+ < Cs+\( \ll \) H+ sequence. The cation conductivity values calculated from the self-diffusion coefficients based on the Nernst–Einstein equation are essentially higher than the experimental values.

INTRODUCTION

The selectivity of sulfocationite membranes to cations of a number of alkali metals is largely determined by the hydration of cations. The first results of hydration in polystyrenedivinylbenzene-based cation exchangers (Dowex 50 W) obtained by NMR spectroscopy were published in the early 1970s [19]. The signals of 1H nuclei of water molecules were shifted to the strong fields because of the polarization of water molecules in the hydration shells of metal cations. In the case of membranes in the H+ form, on the contrary, signals were shifted to the weak fields because cations \({\text{H(}}{{{\text{H}}}_{{\text{2}}}}{\text{O)}}_{h}^{{\text{ + }}}\) (h is the hydration number) were formed. It was shown that at low moisture contents, in the KU-2-8 cation exchangers and membranes based on them [79] an acidic proton forms diaquahydrogen ion \({{{\text{H}}}_{{\text{5}}}}{\text{O}}_{{\text{2}}}^{{\text{ + }}}\) in the perfluorinated sulfation cation exchange membranes Nafion [1017] and MF-4SK [1821].

The diffusion of water molecules and cations, which determines the ionic conductivity, is of particular interest. The diffusion coefficients of water in ion-exchange membranes measured by pulsed field gradient 1H NMR decrease by several orders of magnitude with a decrease in the number of water molecules per sulfo group (λ) below the cation hydration number (h) [10, 20]. The proton conductivity changes in a similar way [10, 2629]. The temperature dependences of the diffusion coefficients are approximated by the Arrhenius equation. For samples with high moisture content (λ > h) at high temperatures, the diffusion activation energy is close to the diffusion activation energy of pure water and increases significantly at low temperatures [10, 20]. At low moisture contents (λ ≈ h), the activation energy of water diffusion in the membranes is greater than that for pure water [10, 20].

The aim of this work was to study the hydration, diffusion of water, Li+, Na+, and Cs+ cations, and the ionic conductivity of MSC membranes made of polyethylene (PE) with grafted sulfonated polystyrene (PS). These membranes have a “heterogeneous” structure consisting of hydrophobic crystalline and amorphous “phases” of PE and a hydrophilic water-swelling “phase” of sulfonated PS. The concept of phase is arbitrary in this case, since they are interconnected by chemical bonds and the interface between them can therefore be drawn with some degree of conventionality. Recent studies have shown that this type of membrane with separated main and grafted phases has high electrochemical characteristics that are not inferior to the homogeneous perfluorinated Nafion membranes [3032]. The data obtained are compared with the corresponding results obtained for the Nafion membrane.

MATERIALS AND METHODS

Sulfocathionite membranes were obtained by post-radiation grafting of styrene on a 20 μm thick pre-peroxidized low-density PE film followed by sulfonation of grafted PS with 96% sulfuric acid as described in [30]. To generate peroxides in a PE film, the latter was irradiated in air at a 60Co γ-radiation source with an irradiation dose rate of 5.2 Gy/s to absorbed irradiation doses of 0.05 and 0.1 MGy.

Post-radiation-chemical grafting polymerization was carried out in a styrene/methanol mixture (1/1 by volume) containing iron(II) sulfate as a peroxide reducing agent. The degree of PS grafting (∆p) was calculated as the weight gain of the film because the formation of grafted PS chains on PE referred to the mass of the initial film:

$$\Delta p = [{{({{m}_{1}} - {{m}_{0}})} \mathord{\left/ {\vphantom {{({{m}_{1}} - {{m}_{0}})} {{{m}_{0}}}}} \right. \kern-0em} {{{m}_{0}}}}] \times 100\% ,$$
((1))

where m1 is the mass of polystyrene grafted sample; m0 is the mass of the sample (PE film) before grafting.

Sulfonation of PE with grafted PS was carried out at a temperature of 98°C, after which the films were successively washed with aqueous solutions with decreasing concentrations of sulfuric acid and distilled water until the washings were neutral. The measurement of the static ion-exchange capacity SEC (mEq/g) was carried out according to the State Standard GOST 20255.1-89 and GOST 20255.2-89. A sample of the dry cation exchange membrane in proton form was weighed and placed in a dry conical flask with a NaOH solution. The flask was sealed with a stopper and stirred for several hours. The NaOH solution was then poured into a dry beaker and the sample was titrated with a standard HCl solution. The calculation of the exchange capacity was carried out according to the standard formula. A membrane was studied with a SEC of 2.0, 2.5, and 4.7 mEq/g.

To determine the moisture content, the membranes were balanced with deionized water or kept over saturated salt solutions. In the case of the membrane being in contact with deionized water, excess water was removed from the sample using filter paper, after which the membrane was weighed. The membrane was then dried at 80°C to constant weight in a vacuum created by a foreline pump. The moisture content of the ion exchange membrane was calculated by mass loss. The moisture content of membranes held over saturated aqueous solutions of salts with different partial pressure of water vapor was determined in a similar way.

To prepare the sample for NMR measurements, the membrane was cut into small strips, weighed, and placed in desiccators containing saturated solutions of salts of ZnCl2 (RH = 10%), MgCl2 (RH = 32%), NaBr (RH = 58%), NaNO2 (RH = 65%), NaCl (RH = 78%), KCl (RH = 86%), Na2CO3 (RH = 95%), and water (RH = 98%). Membrane samples were kept in desiccators until a constant weight. Membranes previously swollen in water were also investigated. For NMR studies, the samples were placed in a standard 5 mm ampoule, which was hermetically sealed. The measurements were carried out in the 25 to –40°С temperature range.

To standardize membranes in the H+ form, the initial samples were kept for 24 hours in a 1 M HCl solution and then washed with distilled water.

To transfer the membrane to the Li+ form, the sample was kept in a 1 M solution of lithium hydroxide (with a tenfold excess) for 24 hours, after which it was thoroughly washed with distilled water, dried in air, placed in a standard 5 mm NMR ampoule, and moistened with water. The completeness of the conversion to the Li+ form was determined by 1H NMR spectra.

To transfer the membrane to the Na+ form, the sample in the Li+ form was kept in a 1 M solution of sodium chloride (with a tenfold excess) for 24 hours, after which it was thoroughly washed with distilled water, dried in air, placed in a standard 5 mm NMR ampoule, and moistened with water. The completeness of the conversion to the Na+ form was determined by 7Li NMR spectra.

To transfer the membrane to the Cs+ form, the sample in the Na+ form was kept for 24 hours in a 1M solution of cesium sulfate (with a tenfold excess) and thoroughly washed with distilled water. The sample was then dried in air, placed in a standard 5 mm NMR ampoule, and moistened with water. The completeness of the conversion to the Cs+ form was determined by 23Na NMR spectra.

The experiments to measure the diffusion coefficients were carried out on a Fourier transform NMR spectrometer Bruker Avance III-400 WB transformation equipped with a pulsed magnetic field gradient sensor; the maximum value of the pulsed gradient was 30 T/m. The stimulated echo pulse sequence was used to measure diffusion coefficients SDCs.

The diffusion coefficients were measured at frequencies of 400.22, 155.51, 105.84, and 52.48 MHz on 1Н, 7Li, 23Na, and 133Cs nuclei, respectively. High-resolution 1Н, 7Li, 23Na, and 133Cs NMR spectra were recorded on a Bruker Avance III-500 NMR spectrometer.

Ion conductivity was measured using an Elins Z1500J impedance meter (frequency range 1 kHz–1.5 MHz) on symmetric carbon/membrane/carbon cells with an active surface area S of 0.5 cm2. The conductivity value σ (Ω–1 cm–1) was calculated from the resistance R found from the impedance hodographs from the cutoff on the axis of active resistances and the geometric dimensions of the membrane according to the following formula σ = l/(SR), where l is the membrane thickness in centimeters. The Binder MKF 115 constant climate chamber was used to set the required humidity and temperature during measurement.

RESULTS AND DISCUSSION

The studied MSC membrane is a thin transparent film with ion-exchange capacities of 2.0, 2.5, and 4.7 mEq per gram of dry membrane. An increase in relative humidity leads to an increase in the moisture content of the membranes (Table 1). The moisture capacity of the membranes substantially depends on the nature of the counterion and increases in the series H > Li > Na > Cs, which is explained by a decrease of the M+–OH2 bond strength and, accordingly, a decrease in the hydration energy in this series [33]. The moisture content of the membranes in the H+ and Li+ ionic forms is almost equal; the number of water molecules per sulfo group λ is about 50, respectively. In the Na+ and Cs+ ionic forms, λ is slightly lower (Table 1); this number of water molecules per sulfo group is sufficient for the cations in the membrane to form the highly symmetric hydrate complex as in a dilute solution. For this reason, the value of the electric field gradient is low, which is accompanied by long spin-spin relaxation times (more than a few milliseconds), which makes it possible to measure the self-diffusion coefficients of the Na+ and Cs+ cations.

Table 1. Moisture content of the MSC membrane in various ionic forms at relative humidity

1H, 7Li, 23Na, and 133Cs NMR Spectroscopy

The 1Н NMR spectra at room temperature consist of two singlet lines (Fig. 1a). The most intense line is assigned to the averaged signal of protons of water molecules and H+ counterions. The signal in the region of 2–3 ppm is sufficiently narrow for the polymer matrix of the membrane, which indicates a high mobility of the fragments that determine it. Based on the magnitude of the chemical shift, it can be assumed that this signal belongs to the –CHx protons (х = 1–3) of the groups of low molecular weight fragments of polyethylene arising during γ irradiation. With increasing humidity, the line of protons of water molecules masks a weak signal of protons of the –CHx groups due to its high intensity.

Fig. 1.
figure1

(a) 1H NMR spectrum of the MSC membrane in the H+ form at a relative humidity of RH = 10% a, (b) 7Li NMR spectrum of the MSC membrane in the Li+ form in contact with water, (c) 23Na NMR spectrum of the MSC membrane in the Na+ form in contact with water, (d) 133Cs NMR spectrum of the MSC membrane in the Cs+ form in contact with water. The measurement temperature was 25°C.

The 7Li, 23Na, and 133Cs NMR spectra of membranes in contact with water are narrow singlet lines (Figs. 1b–1d), which indicates a high mobility of cations.

We note the main features of the behavior of the low-field component in membranes in the H+ form, which is an average NMR signal of H+ cations and protons of water molecules. In the H+ form of MSCs at low moisture contents and low temperatures (below 0°C), the NMR line width is small (no more than 1 kHz), which indicates the high mobility of water molecules and hydrated H+ ions under these conditions (Fig. 1a).

The width of the NMR line increases with decreasing temperature and moisture content, while the NMR line shifts to weak fields. The chemical shift in the membrane is much larger than the chemical shift of the protons of pure water. This results from the hydration of H+ counterions by water molecules, which is characteristic of sulfocationionites in the H+ form, including Nafion membranes [514].

Temperature dependence of chemical shifts of 1H nuclei, structure of hydrated complexes of H+ counterions. Direct information on the hydration of cations in membranes can be obtained from an analysis of the temperature dependences of the chemical shifts of 1H nuclei, which are an average NMR line of H+ counterions (for the H+ ionic form) and water molecules.

Following the methodology for analyzing the temperature dependences of chemical shifts in aqueous solutions of acids and the H+ form of Nafion membranes described in detail in [10], hydration numbers h of H+ counterions were calculated from Eq. (2).

$$h = {\lambda } - \frac{{(0.5 + {\lambda })\frac{{d{\delta }}}{{dT}}}}{{\frac{{d{{{\delta }}_{{{{{\text{H}}}_{{\text{2}}}}{\text{O}}}}}}}{{dT}}}},$$
((2))

where δ is the chemical shift of the low-field 1H component, is the chemical shift of the protons of bulk water, and λ is the number of water molecules per sulfo group.

Figure 2 shows the temperature dependences of proton chemical shifts for MSC membranes. These dependences are linear δ = a – bT and are similar to the corresponding dependences in the Nafion membrane [10]. The hydration numbers calculated from Eq. (2) are given in Table 2. With a low moisture content, the proton hydration number (h) is close to two; with an increase in the degree of hydration, h increases to h ≈ 4. Thus, as in the Nafion membranes [10], at low water contents in the MSC membrane, the H+ cation is strongly bound to two water molecules, forming cation \({{{\text{H}}}_{{\text{5}}}}{\text{O}}_{{\text{2}}}^{{\text{ + }}}{\text{.}}\) These two water molecules cannot be removed from the membrane during drying in vacuum or at high temperatures. With a further increase in moisture content, complex \(\left( {{{{\text{H}}}_{{\text{9}}}}{\text{O}}_{{\text{4}}}^{{\text{ + }}}} \right)\) is formed containing four water molecules.

Fig. 2.
figure2

Temperature dependence of proton chemical shifts in the H+ form of MSC membranes at various relative humidities: λ = 4 (1), 5.1 (2), 6.6 (3), 7 (4), 12.5 (5); b is a parameter characterizing the slope of the dependences δ = a – bT (parameters b are shown in the figure).

Table 2.   Numbers of hydration h of H+ cations in the acidic form of MSC membranes depending on the number of water molecules per sulfo group λ

Diffusion of Water Molecules and Cations

Diffusion of water molecules and H+ counterions. To measure the diffusion coefficients, we analyzed the dependences of the amplitude of the spin echo signals A on the amplitude of the magnetic field gradient g (diffusion attenuation). Examples of diffusion attenuation on 1H nuclei are shown in Fig. 3.

Fig. 3.
figure3

Diffusion attenuation on 1H nuclei in the MSC membrane held at various relative humidities: (1) 10% (D1 = 3.2 × 10–12 m2/s, p1 = 0.97; D2 = 1.2 × 10–13, p2 = 0.03); (2) 32% (D1 = 2.5 × 10–11 m2/s, p1 = 0.94; D2 = 7.6 × 10–12 m2/s, p2 = 0.06); (3) 65% (D1 = 1.5 × 10–10 m2/s, p1 = 0.64; D2 = 7 × 10–11 m2/s, p2 = 0.29; D3 = 1.4 × 10–11 m2/s, p3 = 0.07); (4) 75% (D1 = 2.3 × 10–10 m2/s, p1 = 0.92; D2 = 5.3 × 10–11 m2/s, p2 = 0.08); (5) 86% (D1 = 4.0 × 10–10 m2/s, p1 = 0.81; D2 = 1.4 × 10–10 m2/s, p2 = 0.17, D3 = 1.4 × 10–11 m2/s, p3 = 0.02); (6) membrane in contact with water (D1 = 1.4 × 10–9, p1 = 0.88; D2 = 5.0 × 10–10 m2/s, p2 = 0.07, D3 = 2.6 × 10–12 m2/s, p3 = 0.05). Measurement temperature, 20°C; diffusion time, td = 20 ms.

Diffusion attenuation can be approximated by the sum of exponential components

$$A(g) = \frac{{A(2{\tau },{{{\tau }}_{1}},g{\text{)}}}}{{A(2{\tau },{{{\tau }}_{1}},0{\text{)}}}} = \sum\limits_{i = 1}^m {p_{i}^{'}} \exp ( - {{{\gamma }}^{2}}{{g}^{2}}{{{\delta }}^{2}}{{t}_{d}}{{D}_{{si}}}),$$
((3))

where m is the number of phases in the system, Di is the self-diffusion coefficient (SDC) in the i-th phase, γ is the gyromagnetic ratio, Δ is the interval between the pulses of the magnetic field gradients, δ is the duration of the gradient pulse, g is the amplitude of the magnetic field gradient pulse, and td = ∆ δ/3 is the diffusion time.

$$p_{i}^{'} = {{{{p}_{i}}\exp \left( { - \frac{{2{\tau }}}{{{{T}_{{{\text{2i}}}}}}} - \frac{{{{{\tau }}_{{\text{1}}}}}}{{{{T}_{{1i}}}}}} \right)} \mathord{\left/ {\vphantom {{{{p}_{i}}\exp \left( { - \frac{{2{\tau }}}{{{{T}_{{{\text{2i}}}}}}} - \frac{{{{{\tau }}_{{\text{1}}}}}}{{{{T}_{{1i}}}}}} \right)} {\sum\limits_{i = 1}^m {{{p}_{i}}} }}} \right. \kern-0em} {\sum\limits_{i = 1}^m {{{p}_{i}}} }}\exp \left( { - \frac{{2{\tau }}}{{{{T}_{{2i}}}}} - \frac{{{{{\tau }}_{{\text{1}}}}}}{{{{T}_{{1i}}}}}} \right),$$
$$\sum\limits_{i = 1}^m {{{p}_{i}}} = 1,$$

where pi is the relative number of 1H nuclei (population in the i-th phase) characterized by SDC Di, T1i is the spin-lattice relaxation time, and T2i is the spin-spin relaxation time in the i-th phase. For large times Т1 and Т2, usually pi\(p_{i}^{'}.\)

The diffusion attenuation on 1H nuclei in the membrane was approximated by the sum of two (RH = 10%, RH = 32%, RH = 75%) or three (RH = 65%, RH = 86%) exponents, which are characterized by diffusion coefficients (SDCs) D1, D2, and D3 and relative fractions of molecules р1, р2, and р3. The values of the parameters Di and pi are indicated in the caption to Fig. 3. Diffusion attenuation on 1H nuclei in membranes, both in acidic and salt ionic forms in contact with water, was also complex and was approximated by the sum of three exponentials in accordance with Eq. (3). The value of D1 for them was (1.4 ± 0.1) × 10–9 m2/s, which is close to SDC of pure water. This component obviously refers to external water. The second and third components characterize the mobility of water in the membrane. Since p2\( \gg \)p3, it can be concluded that the behavior of water in the membrane is mainly characterized by the coefficient D2. For membranes held at a relative humidity of less than 100%, there is no pure water phase. In this case, the diffusion of water molecules and H+ cations in the membrane is mainly characterized by the coefficient D1, since the diffusion coefficient D1 and the corresponding population p1 are much higher than the self-diffusion coefficients D2 and D3 and populations p2 and p3. The multicomponent diffusion attenuation of 1H nuclei indicates the heterogeneity of the structure of pores and channels in which water molecules are transported.

The temperature dependence of the diffusion coefficients D in the MSC membrane held at different relative humidity is linearized in the coordinates of the Arrhenius equation (Fig. 4).

Fig. 4.
figure4

Temperature dependence of the diffusion coefficients D measured by pulsed field gradient NMR at different water contents in the MSC membrane: (1) 10%; (2) 32%, (3) 75%.

The main feature of the temperature dependences of the self-diffusion coefficients is an increase in the self-diffusion activation energy with a decrease in moisture content in the entire temperature range. This effect is quite typical for the mobility of the hydrated H+ cation and is due to an increase in the average strength of hydrogen bonds and steric effects [34]. It is noteworthy that there is a knee in the temperature dependence of the diffusion coefficients in the membrane held in water vapor at RH = 75% (curve 3, Fig. 4). It should be noted that a similar knee is also present in the temperature dependence of the membrane conductivity. This can be explained only by the crystallization of water in the central part of the membrane pores, whose concentration of cations is much lower [35]. This is because the concentration of cations rapidly decreases due to electrostatic attraction to negatively charged pore walls as they approach their center. The increase in the activation energy of conductivity is determined by the fact that as the solution freezes, an increasingly large number of acidic protons are excluded from the transfer process. With a decrease in the moisture content of the membranes, the concentration of the intra-pore solution increases, and the fracture temperature decreases, overstepping the studied range [35].

Figure 5 shows the dependences of the product of the area of the NMR signal A and temperature T, which are proportional to the number of mobile water molecules. As can be seen from Fig. 5, at RH less than 86% (λ = 12) within the experimental error, the number of mobile water molecules is independent of temperature in the observed temperature range. This indicates that water at a given moisture content does not form an ice phase, while holding high mobility. Indeed, as was shown in [35], the formation of an ice phase near 0°C for the acidic form of membranes can be observed only at a moisture content of more than 18 water molecules per sulfo group.

Fig. 5.
figure5

Dependence of the amount of mobile water in the H+ form of MSC membranes at different moisture contents in the temperature range from 25 to –40°С. The number of water molecules per sulfo group is λ = 5.1 (1), 7 (2), 8.4 (3), 12.5 (4).

We also measured the diffusion coefficients in MSC membranes in the H+ form with different exchange capacities in contact with water. The diffusion coefficients slightly increased with an increase in the exchange capacity (from 3.0 × 10–10 m2/s at 2 mEq/g to 4.7 × 10–10 m2/s at 4.7 mEq/g). This growth results from an increase in the moisture content of membranes and the formation of a more voluminous and bound system of pores and channels [30].

Based on the Nernst–Einstein relation (Eq. (4)), the diffusion coefficients for various moisture contents were calculated from the values of specific conductivity σ:

$$D = \frac{{{\sigma }kT}}{{N{{e}^{2}}}},$$
((4))

where N is the number of charge carriers, cm3; D is the diffusion coefficient, m2/s; e is the electron charge, 1.9 × 10–19 C; k is the Boltzmann constant, 1.38 × 10–23 J/K; and T is the temperature, K.

Experimental diffusion coefficients and those calculated from Eq. (4) at different moisture contents are shown in Fig. 6.

Fig. 6.
figure6

Diffusion coefficients of H+ cations calculated from the proton conductivity data according to Eq. (4) (lower curve) and the average diffusion coefficients of water molecules and H+ cations measured by pulsed field gradient NMR (upper curve) in the H+ form of the MSC membrane at different moisture contents. RH = 100%; the membrane is in contact with water.

It is noteworthy that the dependences of the diffusion coefficients of the cations calculated from the conductivity and measured by NMR on the moisture content are similar. The values of diffusion coefficients decrease with decreasing relative humidity. This is associated with a decrease in membrane hydration and, as a consequence, a decrease in the diameters of channels connecting nanopores. The values of the diffusion coefficients determined by NMR are slightly higher than those calculated based on the data on conductivity. This is quite typical for ion-exchange membranes and arises because the conductivity is limited by proton transfer in narrower portions (channels) of the membranes, while NMR first characterizes the averaged mobility of protons and water in larger pores [36].

Diffusion of alkali metal cations Li+, Na+, and Cs+ and ionic conductivity in MSC membranes. The diffusion coefficients of Li+, Na+, and Cs+ cations in the corresponding ionic forms of MSC membranes in contact with water were measured by 7Li, 23Na, and 133Cs pulsed field gradient NMR. In salt forms of water-swollen MSC membranes, diffusion attenuation on 1H nuclei of water molecules, as in the acidic form of MSCs, are described by Eq. (3) and are approximated by the sum of three exponentials (Fig. 3, curve 6). As shown above, the behavior of water molecules in a membrane in contact with water is mainly due to the second component of diffusion attenuation, which is characterized by diffusion coefficient D2.

Figure 7 shows the diffusion attenuation on 7Li, 23Na, and 133Cs nuclei for the Li+, Na+, and Cs+ salt forms of MSC membranes. Diffusion attenuation is exponential over the entire decay range of spin echo signals (three decimal orders of magnitude). The diffusion coefficients were determined from Eq. (3) for i = 1. The values of the diffusion coefficients of water molecules and alkali metal cations Li+, Na+, and Cs+ are given in Table 3.

Fig. 7.
figure7

Diffusion attenuation of (a) 7Li nuclei of the Li+ cations, (b) 23Na nuclei of the Na+ cations, (c) 133Cs nuclei of the Cs+ cations in the MSC membrane in contact with water; diffusion time, 20 ms.

Table 3. Experimental diffusion coefficients \({{D}^{{{{{\text{H}}}_{{\text{2}}}}{\text{O}}}}},\)DM+ and those calculated from conductivity for water molecules and Li+, Na+, and Cs+ cations; σexp are experimental values of specific ionic conductivities in the MSC membrane in contact with water

As can be seen from Table 3 and Fig. 6, the conductivity and diffusion coefficient of H+ ions are significantly higher than those for singly charged alkali metal cations, which is due to proton transfer according to the Grotthuss mechanism, which includes cooperative effects [34]. At maximum moisture contents, the diffusion coefficients of alkaline cations calculated from the conductivity increase in the order Li+ < Na+ < Cs+, which is consistent with the diffusion coefficients of cations and water molecules obtained from NMR. In this case, the values of diffusion coefficients determined by NMR, as well as in the case with the acid form of the membranes, are slightly higher than the values calculated based on the data on conductivity. This sequence for the diffusion of cations is the reverse of the sequence of their hydrated radii in aqueous solutions [33]. In the same row, the energy of hydration decreases. The mobility of an ion in a membrane is therefore determined by the ease of its diffusion through the system of pores and channels of the membrane.

CONCLUSIONS

Pulsed field gradient NMR has been used in this work to measure diffusion coefficients of Li+, Na+, and Cs+ counterions in ion-exchange systems. At maximum moisture content, the diffusion coefficients of cations increase in the series Li+ < Na+ < Cs+\( \ll \) Н+.

The experimental dependences of diffusion coefficients on moisture content and temperature found by NMR are in qualitative agreement with the corresponding dependences of diffusion coefficients calculated from data on conductivity. At the same time, the values of diffusion coefficients calculated from the ionic conductivity have been found to be lower than the values measured by pulsed field gradient NMR. The reasons for the patterns found are discussed.

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Funding

This work was supported by the Russian Foundation for Basic Research (project no. 18-08-00423 A). The studies of ionic conductivity were performed using equipment at the Center for Collective Use of the Kurnakov Institute, functioning with the support of the State Assignment of the Kurnakov Institute in the field of fundamental scientific research.

NMR measurements were performed using the equipment of the Center for Collective Use of the Institute of Problems of Chemical Physics with the support of the State Assignment of the Institute (state registration nos. 0089-2019-0010 and 0089-2019-0002).

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Correspondence to V. I. Volkov.

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Translated by V. Avdeeva

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Volkov, V.I., Chernyak, A.V., Golubenko, D.V. et al. Mobility of Cations and Water Molecules in Sulfocation-Exchange Membranes Based on Polyethylene and Sulfonated Grafted Polystyrene. Membr. Membr. Technol. 2, 54–62 (2020). https://doi.org/10.1134/S2517751620010096

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Keywords:

  • sulfocation exchange membrane
  • hydration number
  • diffusion
  • ionic conductivity
  • pulsed field gradient NMR
  • impedance spectroscopy