RSC Advances View Article Online PAPER View Journal | View Issue Dynamic ionic radius of alkali metal ions in aqueous solution: a pulsed-field gradient NMR study† Cite this: RSC Adv.,2021,11,20252 Kikuko Hayamizu, *a Yusuke Chiba b and Tomoyuki Haishic The dynamic behavior of alkali metal ions, Li+,Na+,K+,Rb+ and Cs+ in aqueous solutions is one of the most important topics in solution chemistry. Since these alkali metals contain nuclear magnetic resonance (NMR) active nuclei, it is possible to directly measure the diffusion constants of the alkali metal ions using the pulsed field gradient (PFG) NMR method. In this paper, the 7Li, 23Na, 87Rb, 133Cs and 1H resonances are observed for diffusion constants in aqueous solution and the solvent H2O. Until now, the values of the diffusion constant have been lacking when discussing hydration effects around alkali metal ions. It is known that the static ionic radius (Rion) increases with increasing the atomic number, and the Received 23rd March 2021 experimental diffusion constants also increase with increasing the atomic number, which is opposite to Accepted 19th May 2021 the Stokes–Einstein (SE) relation. It suggests that alkali metal ions diffuse through a space of 10À6 m DOI: 10.1039/d1ra02301b accompanying the hydrated spheres with a time interval of 10À3 s. For each alkali metal ion, the dynamic Creative Commons Attribution 3.0 Unported Licence. rsc.li/rsc-advances ionic radius is evaluated. Introduction neutron diffraction spectroscopy, and belong to macroscopic properties such as viscosity and ionic conductivity. The PFG- The behavior of alkaline salts in aqueous solutions is an NMR method measures positional migration over a space of À important topic in solution chemistry. Hydrated ions in 10 6 m. Although measurements of viscosity and ionic aqueous solutions have been the subject of numerous studies conductivity have been widely conducted, experimental values and fundamental studies have been reviewed.1,2 Various tech- of diffusion constants are limited. This article is licensed under a niques have been continuously used for studies on the hydra- The relationship between the diffusion constant D and the tion of the alkali metal ions, for example, in recent papers, viscosity (h) is known as the Stokes–Einstein (SE) equation: neutron diffraction,3 large-angle X-ray scattering and double- 1 kT Open Access Article. Published on 07 June 2021. Downloaded 9/30/2021 8:03:29 AM. 4 D ¼ ; (1) reference infrared (IR) spectroscopy, oxygen K-edge X-ray crs ph absorption spectroscopy,5 and theoretical approaches.6–8 Most studies are concerned with the short-range effects of the where k is the Boltzmann constant, rs is the Stokes radius of the ff hydration of alkali metal ions. Because these alkali metals di using species, and c is the constant, for which the theoretical include nuclear magnetic resonance (NMR) active nuclei, the ranges are between 4 and 6 for slip and stick boundary condi- 9 diffusion constants could be measured directly using the tions, respectively. ff ff pulsed-eld gradient (PFG) NMR method. In this paper, the 7Li, The PFG-NMR method can a ord directly the di usion 23Na, 87Rb, 133Cs and 1H resonances were observed for the constants of NMR active nuclei. As D is related to the ionic conductivity via the Nernst–Einstein relation, the experimental diffusion constants of the alkali metal ions and the solvent H2O. The diffusion measurements were performed in a time scale of D values of Li solution electrolytes for Li-ion batteries (LIB) have À + 7 19 11 10 3 s and were very long compared with the X-ray, IR, and been piled up for Li ( Li) and anions ( F, B, and others) in organic solvents.10 Ionic liquids are another class of solution electrolyte and we aInstitute of Applied Physics, Tsukuba University, Tennodai, Tsukuba 305-8573, Japan. have reported temperature-dependent physical constants such E-mail: [email protected] as density, ionic conductivity, h, and D for various ionic liquids bGraduate School of Pure and Applied Sciences and Tsukuba Research Center for and Li salt-doped ionic liquids. D is macroscopic in nature, and Energy, Materials Science (TREMS), University of Tsukuba, Tennodai, Tsukuba 305- each electrolyte component has a different value, which can be 8573, Japan measured independently for an individual nucleus. Experi- cMRTechnology, TCI-B5, Sengen, Tsukuba 305-0047, Japan mental values of D relate well with the experimental h by the SE † Electronic supplementary information (ESI) available: The Hahn and stimulated ph echo pulse sequences for the PFG NMR. Measuring conditions of the Hahn-PFG relation. The plots of D versus kT/ are always linear and the ff 1H, 7Li, 23Na, 133Ce and those of STE-PFG for 87Rb with short relaxation times. gradients a ord the experimental values of 1/crs. Discussion on – h The Stokes Einstein plot (D versus kT/p ) of pure H2O, and the rations of DLi the constant c and the Stokes radius rs is necessary for practical and DNa with each solvent DH2O. See DOI: 10.1039/d1ra02301b 20252 | RSC Adv.,2021,11,20252–20257 © 2021 The Author(s). Published by the Royal Society of Chemistry View Article Online Paper RSC Advances T T systems. Reasonable rs values may be calculated by molecular Table 1 Basic properties and 1 and 2 at 303 K for the nuclei of alkali orbital methods, and the c values were evaluated experimentally metal ions in ionic liquid systems. We have reported the experimental c + Frequency values in the SE relation for the cations, anions and solvated Li b À31 2 Nucleus T1 T2 (MHz) I Q (10 m ) in ionic liquids composed of cations, 1-ethyl-3- methylimidazolium (EMIm) and N-methyl-N-propyl- 7Li 25 s 5 s 78.45 3/2 À40.1 23 11,12 Na 46 ms 23 ms 53.39 3/2 104 pyrrolidinium (P13). The anions were bis(tri- 39K 64 ms 32 ms 18.68a 3/2 58.5 uoromethanesulfonyl)amide (TFSA) and bis(uorosulfonyl) 87Rb 1.8 ms 1.2 ms 27.85 3/2 133.5 amide (FSA) and the systems were prepared without and with 133Cs 9 s 1.2 s 26.47 7/2 À3.43 1 doping of a Li salt. Using the temperature-dependent values of H(H2O) 3.5 s — 201.85 1/2 — D and h, the plots of D versus k/ph were always linear. From the a Observed by a JEOL ECZ-400 spectrometer at the eld strength of 9.404 b gradient of 1/crs, experimental value of crs was evaluated for T. Nuclear quadrupole moment from Bruker NMR properties of each component. The c value was estimated assuming that the selected isotopes. rs value is the van del Waals radius of the molecular orbital calculation. The approximate c values were 2.4 to 3.1 for cations (EMIm and P ), 2.7 to 3.7 for anions (TFSA and FSA), and 3.5 to 13 ff 4.5 for the Li+ solvated by anions. In the ionic liquid systems, values are important to determine the di usion measuring the c values of the cation are smaller than those of the anion. It conditions. The PFG NMR pulse sequences are shown for the 1 7 23 133 indicates that the experimental measurable values D and h are Hahn echo pulse sequence ( H, Li, Na, and Ce) and the 87 † well explained by the SE relation, and the cr value is a constant stimulated echo pulse sequence ( Rb) in Fig. S1 in ESI. The T1 s ffi 1 7 23 in each system. It is important to note that c is not a universal and T2 values at 303 K are su ciently long for H, Li, Na, and 133 constant. Cs to use the Hahn-echo PFG NMR pulse sequence and the measurements were performed with the PFG strength 1.26 Creative Commons Attribution 3.0 Unported Licence. In recent years, alkali metals and alkaline earth metals such À1 as Na+,K+,Mg2+, and Ca2+ have been targeted for next- Tm . The precise measurement details are described in the † 87 + generation energy storage systems from the viewpoint of ESI. Because the T1 and T2 values of Rb were extremely resource conservation. To date, organic solvents have been short, the stimulated echo PFG pulse sequence was used with À1 † 39 widely used in LIBs. The possibility of using aqueous solutions the g value of 10.0 Tm (Fig. S2, ESI ). K belongs to a low-g 39 is being explored for the prevention of volatility, in addition of nuclei and a JEOL ECZ-400 spectrometer can measure the K 39 the usages of polymer and solid electrolytes. Similarly, fuel cell spectra at 18.6 MHz. The T1 and T2 values for K were short technology is important in its contribution to power sources. In (Table 1). Unfortunately, the maximum PFG strength equipped À1 39 1988, diffusion coefficients of Li+,Na+, and Cs+ were observed was 0.3 Tm . Several attempts were made to obtain the K This article is licensed under a ff using steady-state eld gradient spin-echo NMR method in di usion constant for the saturated aqueous solution (3 M), but + aqueous solutions.13 Recently, 1H+, 7Li+, 23Na+ and 133Cs+ a reliable D value for K could not be obtained because of poor diffusion constants were measured in cation-exchange decay of the echo attenuation. The repetition time of every 14 + experiment including relaxation time measurement was set at Open Access Article. Published on 07 June 2021. Downloaded 9/30/2021 8:03:29 AM.