Translational diffusion of components in concentrated LiTFSI solutions in acetonitrile according to multinuclear pulse NMR data

Translational diffusion of components in concentrated LiTFSI solutions in acetonitrile according to multinuclear pulse NMR data | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Translational diffusion of components in concentrated LiTFSI solutions in acetonitrile according to multinuclear pulse NMR data Kirill A. Mukhin, Vladimir V. Matveev, Vladimir I. Chizhik This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6959449/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 21 Jul, 2025 Read the published version in Applied Magnetic Resonance → Version 1 posted 9 You are reading this latest preprint version Abstract The diffusion coefficients of solvent molecules, cations and anions in concentrated “LiTFSI–acetonitrile” solutions were measured in the temperature range from − 15 to + 75 o C. The activation energies ( E a ) for diffusion motion of each species were calculated. The features of translational motion in this system are discussed. The data indicate the existence of some predominant structural composition with the molar ratio “salt/ACN”≈1/4.5. The acetonitrile molecules move more freely in the structural "mosaic" than solvated ions. A new approach to describing the concentration dependencies of diffusion coefficients in the case of fast both translational motion and exchange between substructures is suggested. Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 1 Introduction The search for new, more efficient and/or object-oriented liquid electrolytes for lithium batteries (LIBs) is one of the urgent tasks of modern electrochemical and, generally, physico-chemical research. Thus, it was found that with certain mutual combinations of salts and solvent it is possible to increase the content of ions to such an extent that their amount is comparable to the number of solvent molecules, but these objects remain in the liquid state at room temperature. It is currently believed that due to incomplete solvation of cations/anions caused by insufficient amount of solvent molecules, these highly concentrated electrolytes (HCE), unlike related dilute solutions, exhibit beneficial properties, such as wider electrochemical stability windows [ 1 – 4 ], high values of Li + cation transport numbers [ 5 , 6 ], etc. The study of highly concentrated electrolytes of interest to electrochemistry began in the 1960s. At that time, the electrolytes studied were based on water as a solvent and the salts were “common” ones: NaCl, LiCl, CaBr 2 , etc. The salts used in those early studies allowed reaching molar “salt/water” ratios not more than 1:10 (close to saturation). Interest in HCE has recently increased due to the use of highly soluble lithium salts with TFSI- and FSI- anions in electrochemical energy storage systems in general and, in particular, in lithium-ion batteries. The commonly used solvents in HCEs are acetonitrile, carbonates (ethylene carbonate, dimethyl carbonate, propylene carbonate), and water. A number of studies have been conducted in this direction over the past decade, see, for example, [ 7 – 10 ] and references therein. In these works, the authors investigated structure and dynamics of highly concentrated electrolytes using different research methods (SAXS, QENS, MD and other techniques). Analyzing the published results, it can be concluded that there are still quite wide areas for new research in this area, the results of which, combined with the available data, will lead to a better understanding of the structure and dynamics of solutions relevant for electrochemistry. We chose LiTFSI solutions in acetonitrile (ACN) for the study, and the NMR-diffusometry method for characterizing the behavior of components in selected objects. The NMR allows one to measure diffusion coefficients ( D ) for each component in a solution and, thus, to reach more detailed information on the interrelation of transport properties of ions and solvent molecules. The NMR-diffusomertry was successfully applied to a lot of liquid systems (including ionic liquids and HCE/WIS/SIS systems [11‑17]) but as far as we know no studies were undertaken for “LiTFSI-acetonitrile” solutions. In some aspects, the work is a continuation and development of the research presented in Ref. [ 16 , 17 ]. 2 Experimental 2.1 Sample preparation Dry acetonitrile ACN (Sigma-Aldrich, ≤ 10 ppm water content) and lithium bis(trifluoromethanesulfonyl)imide LiTFSI (Acros Organic, 99%) were used for sample preparation. All samples were prepared using the mass method, where an accurately weighed amount of LiTFSI was dissolved in ACN at 25°C. The characteristics of the five prepared samples are presented in Table 1 . Table 1 The characteristics of the samples investigated ( m is the molality, i. e. the number of salt moles per 1kg of a solvent). Sample designation m (LiTFSI) \(\:{m}_{ACN}/\:{m}_{LiTFSI}\) 1 m LiTFSI 1.0 24.4 5 m LiTFSI 5.0 4.9 6 m LiTFSI 6.0 4.1 8 m LiTFSI 8.3 2.9 10 m LiTFSI 10.0 2.4 Before the diffusion coefficient measurements, ¹H NMR spectra were recorded (500 MHz) for the prepared samples. The spectra exhibit a dominant signal from the CH₃-group of acetonitrile and a very weak signal from the water admixture. The integral ratio I(H₂O)/I(CH₃) is below 0.003, which indicates that water is present in the systems in insignificant quantities. 2.2 NMR measurements Among all experimental methods for studying diffusion processes, the NMR one occupies a prominent place, since this method is non-contact and non-destructive, does not require the insertion of any material "tag", allows selective measurements of diffusion coefficients of components in a wide range of values [ 18 – 20 ]. There exist a number of NMR methods for the determination of diffusion coefficients, the Pulsed Field Gradient Stimulated Echo method is used in this work: dstebpgp3s — Double Stimulated Echo with bipolar gradients and 3 spoil-pulses (the magnitude of magnetic gradients is 0 ÷ 50 Gauss/cm, diffusion time is 50 ms). The error in determining the diffusion coefficients was no more than 3%. The temperature range used was from − 15 to + 75 o C. A control experiment with samples of different lengths (standard filling and 1 cm high) showed that convection had insignificant effect on the results of determining diffusion coefficients (see Fig. S2). All NMR experiments were conducted on the basis of Center for Magnetic Resonance in Saint-Petersburg State University using Bruker Avance III 500 MHz. 3 Results and discussion Fig. 1-3 show the typical dependences of the diffusion coefficients of the 1 H, 7 Li and 19 F nuclei on temperature in the “LiTFSI – ACN” solutions (1, 5, and 10 mol/kg ACN). The full set of data is presented in Supplementary Information (SI). As it is obvious from the figures, the diffusion coefficients (CDs) of cations and anions are close but not identical for the minimum salt concentration studied (1 m ). This is indirectly consistent with the findings of the work Ref. [ 9 ] that at low salt concentrations (i.e., with a sufficient number of acetonitrile molecules, see Table 1 ), the TFSI¯ anion prefers to form weak associates with acetonitrile rather than ion pairs with the cation. However, for high concentrations (5 ÷ 10 m ) these DCs practically coincide, which means a strong correlation of the translational motion of ions in the solutions studied. The coincidence of the CDs of the cation and the anion indicates, apparently, the joint diffusion of the counterions in a cluster or domain (like an ionic mosaic with solvent molecules included in it). As it was previously noted in our work [ 17 ], we emphasize that it cannot be a simple contact ion pair, since in this case the solution would have low electrical conductivity (which is not confirmed in experiments). The CDs of acetonitrile significantly exceed the CDs of ions at all concentrations. This means that acetonitrile molecules move more freely in the "mosaic" than solvated ions, that is, the manifestation of the individual behavior of namely acetonitrile molecules differs from the collective one. Since the graphs in Fig. 1 –3 have a rectilinear appearance, one can assume that the activation model is applicable to the objects under study and the activation energy ( E a ) for diffusion motion can be calculated. Since during diffusion over the experiment (50 ms), the components of the solution undergo multiple transitions between different substructures (fast exchange), the E a parameter makes sense of an average parameter that allows us to characterize the average energy barriers for the movement of components in the solution. The calculated E a values are shown in Table 2 and graphically in Fig. 4 . Table 2 The values of activation energies (kJ/mol) for LiTFSI solutions in acetonitrile. 1 m 5 m 6 m 8.3 m 10 m ACN 10.1 ± 0.2 19.1 ± 0.2 21.5 ± 0.3 27.3 ± 0.4 31.8 ± 0.7 7 Li 11.3 ± 0.1 20.4 ± 0.2 22.6 ± 0.2 28.7 ± 0.5 32.6 ± 0.5 19 F 11.6 ± 0.3 20.9 ± 0.7 22.9 ± 0.8 29.6 ± 1.7 32.7 ± 0.9 Before discussing the concentration dependences of the diffusion coefficients, it is advisable to make a few remarks. If there are several states of molecules and/or ions in a system, and a fast (on the time scale of the experiment) molecular exchange is realized between these states, then the diffusion coefficient \(\:{D}_{exp}\) measured in the experiment is usually expressed by a formula, which in the case of two (for simplicity) states has the form (see, for example, [ 21 ]): $$\:{D}_{exp}={p}_{1}{D}_{1}+{p}_{2}{D}_{2}\:,\:\text{w}\text{i}\text{t}\text{h}\:{p}_{1}+{p}_{2}=1,\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:$$ 1 where \(\:{D}_{\text{1,2}\:\:}\) are the diffusion coefficients in states 1 and 2; \(\:{p}_{\text{1,2}\:\:}\) is the relative content of diffusing species in states 1 and 2. In a more convenient form, expression (1) can be rewritten as: $$\:{\:\:\:\:\:\:\:\:\:\:\:\:\:\:D}_{exp}={D}_{1}+{p}_{2}\left({D}_{2}-{D}_{1}\right).$$ 2 It can be seen from formula (2) that if, for example, \(\:{D}_{1}\gg\:\:\) \(\:{D}_{2},\) then the rapidity of the averaged diffusion process is determined to a large extent by the value of \(\:{D}_{1}\) ("faster" structure), which is surprising (both from the point of view of logic and experience). On the other hand, the nuclear magnetic relaxation times ( T 1 and T 2 ) are an important source of information about molecular motion. It is proved [ 18 – 20 ], that in the case of rapid exchange, the NMR relaxation rates (1/ T 1,2 ) are averaged according to a formula similar to (1): (1/ T 1,2 ) exp = p 1 (1/ T 1,2 ) 1 + p 2 (1/ T 1,2 ) 2 . (3) In case of fast movement 1/T 1,2 = const/ D [ 18 – 20 ], and we come to a contradiction between expressions (1, 2) and (3). Since expression (3) leads to a more natural deduction that the average motion under the conditions discussed reflects a greater influence of the slow process, one can conclude: to discuss the effect of increasing the salt content (in our example, p 2 ), it is advisable to use the dependence of 1/ \(\:{D}_{exp}\) on the salt concentration expressed in relative units (or in units of molality). It should be noted that earlier one of the authors of this work developed and successfully applied the approach for studying the microstructure of electrolyte solutions based on the investigation of concentration and temperature dependences of the rates of magnetic relaxation of solvent (and solute) nuclei. A formula of type (3) (for an arbitrary number of states) was used to interpret the experimental data [ 22 ]. The same approach was used in the study of “hydration shells" of CH 2 groups of ω-amino acids in aqueous solutions [ 23 ]. Figures 5 and 6 present the dependences of 1/ \(\:{D}_{exp}\:\) on the concentration of LiTFSI for the nuclei of solvent molecules 1 H (ACN) and 7 Li, 19 F of salt ions. The full set of data is presented in SI. All the graphs show some patterns that are particularly pronounced at low temperatures: the diffusion coefficients of all components decrease by almost 2 orders of magnitude with an increase in the concentration of LiTFSI to 10 mol/kg ACN, and the diffusion coefficients of solvent molecules are approximately in 2–3 times greater than those for ions (in the entire studied concentration range); the graphs show a bend in the region of 5.5 mol/kg of ACN, that is, at the molar ratio “salt/ACN”≈1/4.5, that indicates the existence of some predominant structural composition in the system. These results confirm the conclusions noted during the discussion of temperature dependences. 4 Conclusion The multinuclear NMR-diffusomertry ( 1 H nuclei for solvent molecules, 7 Li and 19 F for salt ions) was applied to the investigation of molecular mobility of all components in concentrated “LiTFSI–acetonitrile” solutions. The evolution of diffusion coefficients in the temperature range from − 15 to + 75 o C is traced. The results obtained indicate that the increase in salt concentration leads to the mobile ionic network ("mosaic") that causes a drastic dynamical slowdown. This model is confirmed by the fact that the activation energies ( E a ) for diffusion motion of acetonitrile molecules, cations and anions are identical. Besides, the diffusion coefficients of cations and anions are very close over the entire concentration range. The data indicate the existence of some predominant structural composition with the molar ratio “salt/ACN” ≈ 1/4.5. Nevertheless, the diffusion coefficients of acetonitrile significantly exceed ones of ions at all concentrations. This means that acetonitrile molecules move more freely in the structural "mosaic" than solvated ions, i.e., the manifestation of the individual behavior of namely acetonitrile molecules differs from the collective one. To specify the structural models, it is planned to conduct computer modeling of microstructure (quantum chemistry and modeling of molecular dynamics). We hope that our experimental data and model discussions will help in the development of safe and promising electrolytes with better electrochemical characteristics. Declarations Acknowledgements NMR measurements were carrying out in the Center for Magnetic Resonance of Research Park of St. Petersburg State University Contributions Kirill A. Mukhin: experiment, data processing, design of the manuscript; Vladimir V. Matveev: idea of experiment, discussion of results, writing; Vladimir I. Chizhik: supervision, idea of interpreting concentration dependencies, writing and editing. Ethical Approval Not applicable to this study. Funding This work was supported by the Russian Science Foundation (project № 23-23-00049). Availability of data and materials Not applicable to this study. References Alvarado J., Schroeder M. A., Zhang M. et al. (2018). A carbonate-free, sulfone-based electrolyte for high-voltage Li-ion batteries. Materials Today, 21(4), 341–353. http://dx.doi.org/10.1016/j.mattod.2018.02.005 Nilsson V., Younesi R., Brandell D., Edström K. and Johansson P. (2018). Critical evaluation of the stability of highly concentrated LiTFSI - Acetonitrile electrolytes vs. graphite, lithium metal and LiFePO 4 electrodes. Journal of Power Sources, 384, 334–341. https://doi.org/10.1016/j.jpowsour.2018.03.019 Dudley J. T., Wilkinson D. P., Thomas G., et al. (1991). Conductivity of electrolytes for rechargeable lithium batteries. 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Supplementary Files SI2025.docx Cite Share Download PDF Status: Published Journal Publication published 21 Jul, 2025 Read the published version in Applied Magnetic Resonance → Version 1 posted Editorial decision: Accepted 09 Jul, 2025 Reviews received at journal 06 Jul, 2025 Reviews received at journal 04 Jul, 2025 Reviewers agreed at journal 30 Jun, 2025 Reviewers agreed at journal 27 Jun, 2025 Reviewers invited by journal 27 Jun, 2025 Editor assigned by journal 25 Jun, 2025 Submission checks completed at journal 24 Jun, 2025 First submitted to journal 23 Jun, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-6959449","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":478395027,"identity":"d481575b-fb8b-40eb-96ca-d5a7288d15ab","order_by":0,"name":"Kirill A. Mukhin","email":"","orcid":"","institution":"St Petersburg University","correspondingAuthor":false,"prefix":"","firstName":"Kirill","middleName":"A.","lastName":"Mukhin","suffix":""},{"id":478395028,"identity":"cae682f0-ddcb-4ba8-902c-bd1a1a5adee0","order_by":1,"name":"Vladimir V. Matveev","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAwElEQVRIiWNgGAWjYFAD9gYGZuJVHwARPAdI1iKRQKQWgwPciZ8/ttnIGdx8/uxxYRtDvsEBglp4N0scbEszNridY248s43BcgMhLZINvBskDpw5nDhzdg6bNG8bgwFBW4BaNv84cOZ//cyZx58Rp4WfgXebxIGKAwn8EgxmRGph5t1mcaYi2bCfB+iXGeckDCQJaWFj7918o8LATp6N/fizxwVlNgZ8hLQgxwUbEEsQUo9mI2nKR8EoGAWjYMQAAATDO8cu1C3AAAAAAElFTkSuQmCC","orcid":"","institution":"St Petersburg University","correspondingAuthor":true,"prefix":"","firstName":"Vladimir","middleName":"V.","lastName":"Matveev","suffix":""},{"id":478395029,"identity":"8b87fec0-70f1-46fb-9c73-8457cc443ab3","order_by":2,"name":"Vladimir I. Chizhik","email":"","orcid":"","institution":"St Petersburg University","correspondingAuthor":false,"prefix":"","firstName":"Vladimir","middleName":"I.","lastName":"Chizhik","suffix":""}],"badges":[],"createdAt":"2025-06-23 19:23:07","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6959449/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6959449/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s00723-025-01774-z","type":"published","date":"2025-07-21T15:58:23+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":85836466,"identity":"39936579-1ab3-4fbe-9341-f8adbb732035","added_by":"auto","created_at":"2025-07-02 08:23:21","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":14354,"visible":true,"origin":"","legend":"\u003cp\u003eThe temperature dependences of diffusion coefficients (\u003cem\u003eD\u003c/em\u003e) for the concentration of 1 mol LiTFSI /kg ACN (\u003csup\u003e1\u003c/sup\u003eH nuclei of solvent molecules, \u003csup\u003e7\u003c/sup\u003eLi and \u003csup\u003e19\u003c/sup\u003eF of salt ions).\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-6959449/v1/89be88b581ee314b56b303a3.png"},{"id":85836453,"identity":"caf448bc-7e80-4578-89ef-1d9e46239102","added_by":"auto","created_at":"2025-07-02 08:23:20","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":14989,"visible":true,"origin":"","legend":"\u003cp\u003eThe temperature dependences of diffusion coefficients (\u003cem\u003eD\u003c/em\u003e) for the concentration of 5 mol LiTFSI /kg ACN (\u003csup\u003e1\u003c/sup\u003eH nuclei of solvent molecules, \u003csup\u003e7\u003c/sup\u003eLi and \u003csup\u003e19\u003c/sup\u003eF of salt ions).\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-6959449/v1/d0a13fbf767fd067a7e6ebbf.png"},{"id":85836467,"identity":"bb116e21-a980-4523-b22b-62dcc16c905a","added_by":"auto","created_at":"2025-07-02 08:23:21","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":14520,"visible":true,"origin":"","legend":"\u003cp\u003eThe temperature dependences of diffusion coefficients (\u003cem\u003eD\u003c/em\u003e) for the concentration of 10 mol LiTFSI /kg ACN (\u003csup\u003e1\u003c/sup\u003eH nuclei of solvent molecules, \u003csup\u003e7\u003c/sup\u003eLi and \u003csup\u003e19\u003c/sup\u003eF of salt ions).\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-6959449/v1/099332937efc1063dc71fc20.png"},{"id":85836459,"identity":"b9cfa171-8d26-49c8-a446-b68a807f5642","added_by":"auto","created_at":"2025-07-02 08:23:20","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":12921,"visible":true,"origin":"","legend":"\u003cp\u003eThe values of activation energies (kJ/mol) for LiTFSI solutions in acetonitrile.\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-6959449/v1/0ce2dd8c8d7a4f5311526e13.png"},{"id":85836428,"identity":"79515ad2-ca9c-4822-a1c0-2c3a769276f4","added_by":"auto","created_at":"2025-07-02 08:23:19","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":23438,"visible":true,"origin":"","legend":"\u003cp\u003eThe dependences of 1/\u003cem\u003eD\u003c/em\u003e\u003csub\u003eexp \u003c/sub\u003eon the concentration of LiTFSI for the nuclei \u003csup\u003e1\u003c/sup\u003eH of solvent molecules\u0026nbsp; (ACN).\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-6959449/v1/9679fa4c17541744eab83b6f.png"},{"id":85836465,"identity":"2f11a7a1-48d9-4403-b109-e621a2b5834f","added_by":"auto","created_at":"2025-07-02 08:23:21","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":18679,"visible":true,"origin":"","legend":"\u003cp\u003eThe dependences of 1/\u003cem\u003eD\u003c/em\u003e\u003csub\u003eexp\u003c/sub\u003e on the concentration of LiTFSI observed for the nuclei \u003csup\u003e1\u003c/sup\u003eH of solvent molecules\u0026nbsp; (ACN) and\u0026nbsp; \u003csup\u003e7\u003c/sup\u003eLi, \u003csup\u003e19\u003c/sup\u003eF of salt ions.\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-6959449/v1/6ec835bb84c1601be1c53b56.png"},{"id":87756786,"identity":"d770c550-ae2b-4807-a657-e9d829cac1bf","added_by":"auto","created_at":"2025-07-28 16:09:16","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":549230,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6959449/v1/3f96bd1f-d1c1-494b-93bd-e5c17d148a20.pdf"},{"id":85836460,"identity":"609457d7-0045-4a3e-b1a9-6a3ddaf7e0da","added_by":"auto","created_at":"2025-07-02 08:23:20","extension":"docx","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":242643,"visible":true,"origin":"","legend":"","description":"","filename":"SI2025.docx","url":"https://assets-eu.researchsquare.com/files/rs-6959449/v1/11db93f2d142d03ff812fd67.docx"}],"financialInterests":"No competing interests reported.","formattedTitle":"Translational diffusion of components in concentrated LiTFSI solutions in acetonitrile according to multinuclear pulse NMR data","fulltext":[{"header":"1 Introduction","content":"\u003cp\u003eThe search for new, more efficient and/or object-oriented liquid electrolytes for lithium batteries (LIBs) is one of the urgent tasks of modern electrochemical and, generally, physico-chemical research. Thus, it was found that with certain mutual combinations of salts and solvent it is possible to increase the content of ions to such an extent that their amount is comparable to the number of solvent molecules, but these objects remain in the liquid state at room temperature. It is currently believed that due to incomplete solvation of cations/anions caused by insufficient amount of solvent molecules, these highly concentrated electrolytes (HCE), unlike related dilute solutions, exhibit beneficial properties, such as wider electrochemical stability windows [\u003cspan additionalcitationids=\"CR2 CR3\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e], high values of Li\u003csup\u003e+\u003c/sup\u003e cation transport numbers [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e], etc.\u003c/p\u003e \u003cp\u003eThe study of highly concentrated electrolytes of interest to electrochemistry began in the 1960s. At that time, the electrolytes studied were based on water as a solvent and the salts were \u0026ldquo;common\u0026rdquo; ones: NaCl, LiCl, CaBr\u003csub\u003e2\u003c/sub\u003e, etc. The salts used in those early studies allowed reaching molar \u0026ldquo;salt/water\u0026rdquo; ratios not more than 1:10 (close to saturation).\u003c/p\u003e \u003cp\u003eInterest in HCE has recently increased due to the use of highly soluble lithium salts with TFSI- and FSI- anions in electrochemical energy storage systems in general and, in particular, in lithium-ion batteries. The commonly used solvents in HCEs are acetonitrile, carbonates (ethylene carbonate, dimethyl carbonate, propylene carbonate), and water. A number of studies have been conducted in this direction over the past decade, see, for example, [\u003cspan additionalcitationids=\"CR8 CR9\" citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e] and references therein. In these works, the authors investigated structure and dynamics of highly concentrated electrolytes using different research methods (SAXS, QENS, MD and other techniques).\u003c/p\u003e \u003cp\u003eAnalyzing the published results, it can be concluded that there are still quite wide areas for new research in this area, the results of which, combined with the available data, will lead to a better understanding of the structure and dynamics of solutions relevant for electrochemistry. We chose LiTFSI solutions in acetonitrile (ACN) for the study, and the NMR-diffusometry method for characterizing the behavior of components in selected objects. The NMR allows one to measure diffusion coefficients (\u003cem\u003eD\u003c/em\u003e) for each component in a solution and, thus, to reach more detailed information on the interrelation of transport properties of ions and solvent molecules. The NMR-diffusomertry was successfully applied to a lot of liquid systems (including ionic liquids and HCE/WIS/SIS systems [11‑17]) but as far as we know no studies were undertaken for \u0026ldquo;LiTFSI-acetonitrile\u0026rdquo; solutions. In some aspects, the work is a continuation and development of the research presented in Ref. [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e, \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e].\u003c/p\u003e"},{"header":"2 Experimental","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1 Sample preparation\u003c/h2\u003e \u003cp\u003eDry acetonitrile ACN (Sigma-Aldrich, \u0026le;\u0026thinsp;10 ppm water content) and lithium bis(trifluoromethanesulfonyl)imide LiTFSI (Acros Organic, 99%) were used for sample preparation. All samples were prepared using the mass method, where an accurately weighed amount of LiTFSI was dissolved in ACN at 25\u0026deg;C. The characteristics of the five prepared samples are presented in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eThe characteristics of the samples investigated (\u003cem\u003em\u003c/em\u003e is the molality, i. e. the number of salt moles per 1kg of a solvent).\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSample designation\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003em\u003c/em\u003e (LiTFSI)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{m}_{ACN}/\\:{m}_{LiTFSI}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u003cem\u003em\u003c/em\u003e LiTFSI\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e24.4\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e5\u003cem\u003em\u003c/em\u003e LiTFSI\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e5.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e4.9\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e6\u003cem\u003em\u003c/em\u003e LiTFSI\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e6.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e4.1\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e8\u003cem\u003em\u003c/em\u003e LiTFSI\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e8.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e2.9\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e10\u003cem\u003em\u003c/em\u003e LiTFSI\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e10.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e2.4\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eBefore the diffusion coefficient measurements, \u0026sup1;H NMR spectra were recorded (500 MHz) for the prepared samples. The spectra exhibit a dominant signal from the CH₃-group of acetonitrile and a very weak signal from the water admixture. The integral ratio I(H₂O)/I(CH₃) is below 0.003, which indicates that water is present in the systems in insignificant quantities.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2 NMR measurements\u003c/h2\u003e \u003cp\u003eAmong all experimental methods for studying diffusion processes, the NMR one occupies a prominent place, since this method is non-contact and non-destructive, does not require the insertion of any material \"tag\", allows selective measurements of diffusion coefficients of components in a wide range of values [\u003cspan additionalcitationids=\"CR19\" citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]. There exist a number of NMR methods for the determination of diffusion coefficients, the Pulsed Field Gradient Stimulated Echo method is used in this work: dstebpgp3s \u0026mdash; Double Stimulated Echo with bipolar gradients and 3 spoil-pulses (the magnitude of magnetic gradients is 0\u0026thinsp;\u0026divide;\u0026thinsp;50 Gauss/cm, diffusion time is 50 ms). The error in determining the diffusion coefficients was no more than 3%. The temperature range used was from \u0026minus;\u0026thinsp;15 to +\u0026thinsp;75\u003csup\u003eo\u003c/sup\u003eC. A control experiment with samples of different lengths (standard filling and 1 cm high) showed that convection had insignificant effect on the results of determining diffusion coefficients (see Fig. S2).\u003c/p\u003e \u003cp\u003eAll NMR experiments were conducted on the basis of Center for Magnetic Resonance in Saint-Petersburg State University using Bruker Avance III 500 MHz.\u003c/p\u003e \u003c/div\u003e"},{"header":"3 Results and discussion","content":"\u003cp\u003eFig. 1-3 show the typical dependences of the diffusion coefficients of the \u003csup\u003e1\u003c/sup\u003eH, \u003csup\u003e7\u003c/sup\u003eLi and \u003csup\u003e19\u003c/sup\u003eF nuclei on temperature in the \u0026ldquo;LiTFSI \u0026ndash; ACN\u0026rdquo; solutions (1, 5, and 10 mol/kg ACN). The full set of data is presented in Supplementary Information (SI). \u003c/p\u003e\u003cp\u003eAs it is obvious from the figures, the diffusion coefficients (CDs) of cations and anions are close but not identical for the minimum salt concentration studied (1\u003cem\u003em\u003c/em\u003e). This is indirectly consistent with the findings of the work Ref. [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e] that at low salt concentrations (i.e., with a sufficient number of acetonitrile molecules, see Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e), the TFSI\u0026macr; anion prefers to form weak associates with acetonitrile rather than ion pairs with the cation. However, for high concentrations (5\u0026thinsp;\u0026divide;\u0026thinsp;10 \u003cem\u003em\u003c/em\u003e) these DCs practically coincide, which means a strong correlation of the translational motion of ions in the solutions studied. The coincidence of the CDs of the cation and the anion indicates, apparently, the joint diffusion of the counterions in a cluster or domain (like an ionic mosaic with solvent molecules included in it). As it was previously noted in our work [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e], we emphasize that it cannot be a simple contact ion pair, since in this case the solution would have low electrical conductivity (which is not confirmed in experiments).\u003c/p\u003e \u003cp\u003eThe CDs of acetonitrile significantly exceed the CDs of ions at all concentrations. This means that acetonitrile molecules move more freely in the \"mosaic\" than solvated ions, that is, the manifestation of the individual behavior of namely acetonitrile molecules differs from the collective one.\u003c/p\u003e \u003cp\u003eSince the graphs in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e1\u003c/span\u003e\u0026ndash;3 have a rectilinear appearance, one can assume that the activation model is applicable to the objects under study and the activation energy (\u003cem\u003eE\u003c/em\u003e\u003csub\u003ea\u003c/sub\u003e) for diffusion motion can be calculated. Since during diffusion over the experiment (50 ms), the components of the solution undergo multiple transitions between different substructures (fast exchange), the \u003cem\u003eE\u003c/em\u003e\u003csub\u003ea\u003c/sub\u003e parameter makes sense of an average parameter that allows us to characterize the average energy barriers for the movement of components in the solution. The calculated \u003cem\u003eE\u003c/em\u003e\u003csub\u003ea\u003c/sub\u003e values are shown in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e and graphically in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eThe values of activation energies (kJ/mol) for LiTFSI solutions in acetonitrile.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\"\u0026plusmn;\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\"\u0026plusmn;\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\"\u0026plusmn;\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\"\u0026plusmn;\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\"\u0026plusmn;\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1\u003cem\u003em\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e5\u003cem\u003em\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e6\u003cem\u003em\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e8.3\u003cem\u003em\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003e10\u003cem\u003em\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eACN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e \u003cp\u003e10.1\u0026thinsp;\u0026plusmn;\u0026thinsp;0.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c3\"\u003e \u003cp\u003e19.1\u0026thinsp;\u0026plusmn;\u0026thinsp;0.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c4\"\u003e \u003cp\u003e21.5\u0026thinsp;\u0026plusmn;\u0026thinsp;0.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c5\"\u003e \u003cp\u003e27.3\u0026thinsp;\u0026plusmn;\u0026thinsp;0.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c6\"\u003e \u003cp\u003e31.8\u0026thinsp;\u0026plusmn;\u0026thinsp;0.7\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003csup\u003e7\u003c/sup\u003eLi\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e \u003cp\u003e11.3\u0026thinsp;\u0026plusmn;\u0026thinsp;0.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c3\"\u003e \u003cp\u003e20.4\u0026thinsp;\u0026plusmn;\u0026thinsp;0.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c4\"\u003e \u003cp\u003e22.6\u0026thinsp;\u0026plusmn;\u0026thinsp;0.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c5\"\u003e \u003cp\u003e28.7\u0026thinsp;\u0026plusmn;\u0026thinsp;0.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c6\"\u003e \u003cp\u003e32.6\u0026thinsp;\u0026plusmn;\u0026thinsp;0.5\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003csup\u003e19\u003c/sup\u003eF\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e \u003cp\u003e11.6\u0026thinsp;\u0026plusmn;\u0026thinsp;0.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c3\"\u003e \u003cp\u003e20.9\u0026thinsp;\u0026plusmn;\u0026thinsp;0.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c4\"\u003e \u003cp\u003e22.9\u0026thinsp;\u0026plusmn;\u0026thinsp;0.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c5\"\u003e \u003cp\u003e29.6\u0026thinsp;\u0026plusmn;\u0026thinsp;1.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c6\"\u003e \u003cp\u003e32.7\u0026thinsp;\u0026plusmn;\u0026thinsp;0.9\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eBefore discussing the concentration dependences of the diffusion coefficients, it is advisable to make a few remarks. If there are several states of molecules and/or ions in a system, and a fast (on the time scale of the experiment) molecular exchange is realized between these states, then the diffusion coefficient \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{D}_{exp}\\)\u003c/span\u003e\u003c/span\u003e measured in the experiment is usually expressed by a formula, which in the case of two (for simplicity) states has the form (see, for example, [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]):\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:{D}_{exp}={p}_{1}{D}_{1}+{p}_{2}{D}_{2}\\:,\\:\\text{w}\\text{i}\\text{t}\\text{h}\\:{p}_{1}+{p}_{2}=1,\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{D}_{\\text{1,2}\\:\\:}\\)\u003c/span\u003e\u003c/span\u003e are the diffusion coefficients in states 1 and 2; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{p}_{\\text{1,2}\\:\\:}\\)\u003c/span\u003e\u003c/span\u003e is the relative content of diffusing species in states 1 and 2. In a more convenient form, expression (1) can be rewritten as:\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\:{\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:D}_{exp}={D}_{1}+{p}_{2}\\left({D}_{2}-{D}_{1}\\right).$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eIt can be seen from formula (2) that if, for example, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{D}_{1}\\gg\\:\\:\\)\u003c/span\u003e\u003c/span\u003e \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{D}_{2},\\)\u003c/span\u003e\u003c/span\u003e then the rapidity of the averaged diffusion process is determined to a large extent by the value of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{D}_{1}\\)\u003c/span\u003e\u003c/span\u003e (\"faster\" structure), which is surprising (both from the point of view of logic and experience).\u003c/p\u003e \u003cp\u003eOn the other hand, the nuclear magnetic relaxation times (\u003cem\u003eT\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e and \u003cem\u003eT\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e) are an important source of information about molecular motion. It is proved [\u003cspan additionalcitationids=\"CR19\" citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e], that in the case of rapid exchange, the NMR relaxation rates (1/\u003cem\u003eT\u003c/em\u003e\u003csub\u003e1,2\u003c/sub\u003e) are averaged according to a formula similar to (1):\u003c/p\u003e \u003cp\u003e(1/\u003cem\u003eT\u003c/em\u003e\u003csub\u003e1,2\u003c/sub\u003e)\u003csub\u003eexp\u003c/sub\u003e = \u003cem\u003ep\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e (1/\u003cem\u003eT\u003c/em\u003e\u003csub\u003e1,2\u003c/sub\u003e)\u003csub\u003e1\u003c/sub\u003e + \u003cem\u003ep\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e (1/\u003cem\u003eT\u003c/em\u003e\u003csub\u003e1,2\u003c/sub\u003e)\u003csub\u003e2\u003c/sub\u003e. (3)\u003c/p\u003e \u003cp\u003eIn case of fast movement 1/T\u003csub\u003e1,2\u003c/sub\u003e = const/\u003cem\u003eD\u003c/em\u003e [\u003cspan additionalcitationids=\"CR19\" citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e], and we come to a contradiction between expressions (1, 2) and (3). Since expression (3) leads to a more natural deduction that the average motion under the conditions discussed reflects a greater influence of the slow process, one can conclude: to discuss the effect of increasing the salt content (in our example, \u003cem\u003ep\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e), it is advisable to use the dependence of 1/\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{D}_{exp}\\)\u003c/span\u003e\u003c/span\u003e on the salt concentration expressed in relative units (or in units of molality). It should be noted that earlier one of the authors of this work developed and successfully applied the approach for studying the microstructure of electrolyte solutions based on the investigation of concentration and temperature dependences of the rates of magnetic relaxation of solvent (and solute) nuclei. A formula of type (3) (for an arbitrary number of states) was used to interpret the experimental data [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e]. The same approach was used in the study of \u0026ldquo;hydration shells\" of CH\u003csub\u003e2\u003c/sub\u003e groups of ω-amino acids in aqueous solutions [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eFigures \u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e and \u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e present the dependences of 1/\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{D}_{exp}\\:\\)\u003c/span\u003e\u003c/span\u003eon the concentration of LiTFSI for the nuclei of solvent molecules \u003csup\u003e1\u003c/sup\u003eH (ACN) and \u003csup\u003e7\u003c/sup\u003eLi, \u003csup\u003e19\u003c/sup\u003eF of salt ions. The full set of data is presented in SI. All the graphs show some patterns that are particularly pronounced at low temperatures:\u003c/p\u003e \u003cp\u003e \u003col\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003ethe diffusion coefficients of all components decrease by almost 2 orders of magnitude with an increase in the concentration of LiTFSI to 10 mol/kg ACN, and the diffusion coefficients of solvent molecules are approximately in 2\u0026ndash;3 times greater than those for ions (in the entire studied concentration range);\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003ethe graphs show a bend in the region of 5.5 mol/kg of ACN, that is, at the molar ratio \u0026ldquo;salt/ACN\u0026rdquo;\u0026asymp;1/4.5, that indicates the existence of some predominant structural composition in the system.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003c/ol\u003e \u003c/p\u003e \u003cp\u003eThese results confirm the conclusions noted during the discussion of temperature dependences.\u003c/p\u003e "},{"header":"4 Conclusion","content":"\u003cp\u003eThe multinuclear NMR-diffusomertry (\u003csup\u003e1\u003c/sup\u003eH nuclei for solvent molecules, \u003csup\u003e7\u003c/sup\u003eLi and \u003csup\u003e19\u003c/sup\u003eF for salt ions) was applied to the investigation of molecular mobility of all components in concentrated \u0026ldquo;LiTFSI\u0026ndash;acetonitrile\u0026rdquo; solutions. The evolution of diffusion coefficients in the temperature range from \u0026minus;\u0026thinsp;15 to +\u0026thinsp;75\u003csup\u003eo\u003c/sup\u003eC is traced. The results obtained indicate that the increase in salt concentration leads to the mobile ionic network (\"mosaic\") that causes a drastic dynamical slowdown. This model is confirmed by the fact that the activation energies (\u003cem\u003eE\u003c/em\u003e\u003csub\u003ea\u003c/sub\u003e) for diffusion motion of acetonitrile molecules, cations and anions are identical. Besides, the diffusion coefficients of cations and anions are very close over the entire concentration range. The data indicate the existence of some predominant structural composition with the molar ratio \u0026ldquo;salt/ACN\u0026rdquo; \u0026asymp; 1/4.5. Nevertheless, the diffusion coefficients of acetonitrile significantly exceed ones of ions at all concentrations. This means that acetonitrile molecules move more freely in the structural \"mosaic\" than solvated ions, i.e., the manifestation of the individual behavior of namely acetonitrile molecules differs from the collective one. To specify the structural models, it is planned to conduct computer modeling of microstructure (quantum chemistry and modeling of molecular dynamics).\u003c/p\u003e \u003cp\u003eWe hope that our experimental data and model discussions will help in the development of safe and promising electrolytes with better electrochemical characteristics.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eAcknowledgements\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNMR measurements were carrying out in the Center for Magnetic Resonance of Research Park of St. Petersburg State University\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eContributions\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eKirill A. Mukhin: experiment, data processing,\u0026nbsp;design of the manuscript;\u003c/p\u003e\n\u003cp\u003eVladimir V. Matveev: idea of experiment, discussion of results, writing;\u003c/p\u003e\n\u003cp\u003eVladimir I. Chizhik: supervision, idea of interpreting concentration dependencies, writing and editing.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eEthical Approval\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNot applicable to this study.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis work was supported by the Russian Science Foundation (project № 23-23-00049).\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAvailability of data and materials\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNot applicable to this study.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eAlvarado J., Schroeder M. A., Zhang M. et al. (2018). A carbonate-free, sulfone-based electrolyte for high-voltage Li-ion batteries. Materials Today, 21(4), 341\u0026ndash;353. http://dx.doi.org/10.1016/j.mattod.2018.02.005 \u003c/li\u003e\n\u003cli\u003eNilsson V., Younesi R., Brandell D., Edstr\u0026ouml;m K. and Johansson P. (2018). Critical evaluation of the stability of highly concentrated LiTFSI - Acetonitrile electrolytes vs. graphite, lithium metal and LiFePO 4 electrodes. Journal of Power Sources, 384, 334\u0026ndash;341. https://doi.org/10.1016/j.jpowsour.2018.03.019 \u003c/li\u003e\n\u003cli\u003eDudley J. T., Wilkinson D. P., Thomas G., et al. (1991). Conductivity of electrolytes for rechargeable lithium batteries. Journal of Power Sources, 35(1), 59\u0026ndash;82. https://doi.org/10.1016/0378-7753(91)80004-H \u003c/li\u003e\n\u003cli\u003ePetibon R., Aiken C. P., Ma L., Xiong D. and Dahn J. R. (2015). The use of ethyl acetate as a sole solvent in highly concentrated electrolyte for Li-ion batteries. Electrochimica Acta, 154, 287\u0026ndash;293. https://doi.org/10.1016/j.electacta.2014.12.093 \u003c/li\u003e\n\u003cli\u003eIamprasertkun P., Ejigu A. and Dryfe R. (2020). Understanding the Electrochemistry of \u0026ldquo;Water-in-salt\u0026rdquo; Electrolytes: Basal Plane Highly Ordered Pyrolytic Graphite as a Model System. Chemical Science. https://doi.org/10.1039/D0SC01754J \u003c/li\u003e\n\u003cli\u003eMontenegro M. I. and Pletcher D. (1986). The determination of the kinetics of electron transfer using fast sweep cyclic voltammetry at microdisc electrodes. Journal of Electroanalytical Chemistry and Interfacial Electrochemistry, 200(1-2), 371\u0026ndash;374. https://doi.org/10.1016/0022-0728(86)90069-0 \u003c/li\u003e\n\u003cli\u003eLundin F., Aguilera L., Hansen H. W., et al. (2021). Structure and dynamics of highly concentrated LiTFSI/acetonitrile electrolytes. Physical Chemistry Chemical Physics, 23(25), 13819\u0026ndash;13826. https://doi.org/10.1039/D1CP02006D \u003c/li\u003e\n\u003cli\u003eNilsson V., Kotronia A., Lacey M. J., Edstrom, K. and Johansson P. (2020). Highly concentrated LiTFSI \u0026ndash; EC electrolytes for Li metal batteries. ACS Applied Energy Materials, 3, 200-207. https://doi.org/10.1021/acsaem.9b01203 \u003c/li\u003e\n\u003cli\u003eXinyi L., Shao-Chun L., Soenke S., Randall E. W., Y Z and Tao L. (2023). Relationship of the Molecular Structure and Transport Properties of Imide-Based Lithium Salts of \u0026ldquo;Acetonitrile/Water-in-Salt\u0026rdquo; Electrolytes. Chemistry of Materials, 35(16), 6415\u0026ndash;6422. https://doi.org/10.1021/acs.chemmater.3c01148 \u003c/li\u003e\n\u003cli\u003eMa L. and Jiang J. (2024). Vehicular Motions Dominate the Ion Transport in Concentrated LiTFSI Aqueous Solutions? J Phys Chem Lett., 15(17), 4531-4537. https://doi.org/10.1021/acs.jpclett.4c00791 \u003c/li\u003e\n\u003cli\u003eDamodaran K. (2022). Recent advances in NMR spectroscopy of ionic liquids. Progress in Nuclear Magnetic Resonance Spectroscopy, 129, 1\u0026ndash;27. https://doi.org/10.1016/j.pnmrs.2021.12.001 \u003c/li\u003e\n\u003cli\u003eKumar V., Reddy R. R., Kumar B. V. N. P. et al. (2019). Lithium speciation in the LiPF\u003csub\u003e6\u003c/sub\u003e/PC electrolyte studied by two-dimensional heteronuclear overhauser enhancement and pulse-field gradient diffusometry NMR. J. Phys. Chem. C, 123, 9661\u0026ndash;9672. https://doi.org/10.1021/acs.jpcc.8b11599 \u003c/li\u003e\n\u003cli\u003eBaranauskaite V., Pestova O., Vovk M., Matveev V. and L\u0026auml;hderanta E. (2019). Local dynamics in LiCl\u0026ndash;CsCl\u0026ndash;D\u003csub\u003e2\u003c/sub\u003eO water-in-salt solutions according to NMR relaxation. Physical Chemistry Chemical Physics. https://doi.org/10.1039/C9CP03878G \u003c/li\u003e\n\u003cli\u003eIshikawa T., Sudoh T., Shigenobu K. et al. (2025). Weakly coordinating monoether-based concentrated electrolytes: effects of frustrated Li ion coordination on ion transport and Li metal battery performance. Electrochimica Acta, 527, 146234. https://doi.org/10.1016/j.electacta.2025.146234 \u003c/li\u003e\n\u003cli\u003eTyutyukin K.V., Ievlev A.V., Matveev V.V. et al. (2024). Molecular Mobility Study of 1-Butyl-1-Methylpyrrolidinium Bis(trifluoromethylsulfonyl)imide Ionic Liquid by NMR Diffusometry. Appl Magn Reson., 55, 785\u0026ndash;794. https://doi.org/10.1007/s00723-024-01678-4 \u003c/li\u003e\n\u003cli\u003eMatveev V.V., Pestova O.N., Tyutyukin K.V. and Chizhik V.I. (2023). Molecular Mobility in Mixed \u0026ldquo;Water-in-Salt\u0026rdquo; Solutions of LiOAc and KOAc According to NMR Data. Applied Magnetic Resonance, 54(10), 971\u0026ndash;978. https://doi.org/10.1007/s00723-023-01558-3 \u003c/li\u003e\n\u003cli\u003eMukhin K.A., Pestova O.N., Matveev V.V. and Chizhik V.I. (2024). Translational Mobility in Ternary Systems \u0026ldquo;Lithium Acetate\u0026ndash;Cesium Acetate\u0026ndash;Water\u0026rdquo; According to PFG NMR Data. Applied Magnetic Resonance, 55(8), 775\u0026ndash;783. https://doi.org/10.1007/s00723-024-01670-y \u003c/li\u003e\n\u003cli\u003eAbragam A. (1961). The Principles of Nuclear Magnetism. Oxford University Press, Amen House, Londond.\u003c/li\u003e\n\u003cli\u003eSlichter C. P. (1980). Principles of Magnetic Resonance. Springer-Verlag Berlin Heidelberg New York, 655 pp.\u003c/li\u003e\n\u003cli\u003eChizhik V.I., Chernyshev Y. S., Donets A. V. et al. (2014). Magnetic Resonance and Its Applications. Springer-Verlag. 782 pp. https://doi.org/10.1007/978-3-319-05299-1 \u003c/li\u003e\n\u003cli\u003eWijesekera D., Stait‐Gardner T., Gupta A. et al. (2018). A complete derivation of the K\u0026auml;rger equations for analyzing NMR diffusion measurements of exchanging systems. Concepts in Magnetic Resonance Part A, 47A(2), e21468. https://doi.org/10.1002/cmr.a.21468 \u003c/li\u003e\n\u003cli\u003eChizhik V. I. (1997). NMR relaxation and microstructure of aqueous electrolytesolutions. Molecular Physics, 90:4, 653-660. Doi: 10.1080/002689797172363\u003c/li\u003e\n\u003cli\u003eRabdano S. O., Donets A. V., Vovk M. A. et al. (2015). \u0026ldquo;Hydration Shells\u0026rdquo; of CH\u003csub\u003e2 \u003c/sub\u003eGroups of \u0026omega;-Amino Acids as Studied by Deuteron NMR Relaxation. Journal of Physical Chemistry B, 119, 13358\u0026ndash;13366. https://doi.org/10.1021/acs.jpcb.5b06584 \u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"applied-magnetic-resonance","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"apmr","sideBox":"Learn more about [Applied Magnetic Resonance](http://link.springer.com/journal/723)","snPcode":"723","submissionUrl":"https://submission.nature.com/new-submission/723/3","title":"Applied Magnetic Resonance","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-6959449/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6959449/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe diffusion coefficients of solvent molecules, cations and anions in concentrated \u0026ldquo;LiTFSI\u0026ndash;acetonitrile\u0026rdquo; solutions were measured in the temperature range from \u0026minus;\u0026thinsp;15 to +\u0026thinsp;75\u003csup\u003eo\u003c/sup\u003eC. The activation energies (\u003cem\u003eE\u003c/em\u003e\u003csub\u003ea\u003c/sub\u003e) for diffusion motion of each species were calculated. The features of translational motion in this system are discussed. The data indicate the existence of some predominant structural composition with the molar ratio \u0026ldquo;salt/ACN\u0026rdquo;\u0026asymp;1/4.5. The acetonitrile molecules move more freely in the structural \"mosaic\" than solvated ions. A new approach to describing the concentration dependencies of diffusion coefficients in the case of fast both translational motion and exchange between substructures is suggested.\u003c/p\u003e","manuscriptTitle":"Translational diffusion of components in concentrated LiTFSI solutions in acetonitrile according to multinuclear pulse NMR data","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-07-02 08:23:08","doi":"10.21203/rs.3.rs-6959449/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Accepted","date":"2025-07-09T04:50:34+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-07-06T08:42:04+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-07-04T12:51:59+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"203649203230769989403892377241530441419","date":"2025-06-30T11:19:08+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"306264960423614371882964368092328086700","date":"2025-06-27T21:28:05+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-06-27T15:20:21+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-06-25T08:31:24+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-06-24T11:00:36+00:00","index":"","fulltext":""},{"type":"submitted","content":"Applied Magnetic Resonance","date":"2025-06-23T19:08:36+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"applied-magnetic-resonance","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"apmr","sideBox":"Learn more about [Applied Magnetic Resonance](http://link.springer.com/journal/723)","snPcode":"723","submissionUrl":"https://submission.nature.com/new-submission/723/3","title":"Applied Magnetic Resonance","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"5d1b9293-c801-4f3b-86a0-82b55aa598c5","owner":[],"postedDate":"July 2nd, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2025-07-28T16:04:40+00:00","versionOfRecord":{"articleIdentity":"rs-6959449","link":"https://doi.org/10.1007/s00723-025-01774-z","journal":{"identity":"applied-magnetic-resonance","isVorOnly":false,"title":"Applied Magnetic Resonance"},"publishedOn":"2025-07-21 15:58:23","publishedOnDateReadable":"July 21st, 2025"},"versionCreatedAt":"2025-07-02 08:23:08","video":"","vorDoi":"10.1007/s00723-025-01774-z","vorDoiUrl":"https://doi.org/10.1007/s00723-025-01774-z","workflowStages":[]},"version":"v1","identity":"rs-6959449","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6959449","identity":"rs-6959449","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}