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Marshenya SN, Dembitskiy AD, Fedorov DS, Scherbakov AG, Trussov IA, Emelianova O, Aksyonov DA, Buzlukov AL, Zhuravlev NA, Denisova TA, Medvedeva NI, Abakumov AM, Antipov EV, Fedotov SS. NaGaPO 4F - a KTiOPO 4-structured solid sodium-ion conductor. Dalton Trans 2023; 52:17426-17437. [PMID: 37947446 DOI: 10.1039/d3dt03107a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2023]
Abstract
Advanced ionic conductors are crucial for a large variety of contemporary technologies spanning solid state ion batteries, fuel cells, gas sensors, water desalination, etc. In this work, we report on a new member of KTiOPO4-structured materials, NaGaPO4F, with sodium-ion conductivity. NaGaPO4F has been obtained for the first time via a facile two-step synthesis consisting of a hydrothermal preparation of an ammonia-based precursor, NH4GaPO4F, followed by an ion exchange reaction with NaNO3. Its crystal structure was precisely refined using a combination of synchrotron X-ray powder diffraction and electron diffraction tomography. The material is thermally stable upon 450 °C showing no significant structural transformations or degradation but only a ∼1% cell volume expansion. Na-ion mobility in NaGaPO4F was investigated by a joint experimental and computational approach comprising solid-state nuclear magnetic resonance (NMR) and density functional theory (DFT). DFT and bond-valence site energy (BVSE) calculations reveal 3D diffusion of sodium in the [GaPO4F] framework with migration barriers amounting to 0.22 and 0.44 eV, respectively, while NMR yields 0.3-0.5 eV that, being coupled with a calculated bandgap of ∼4.25 eV, makes NaGaPO4F a promising fast Na-ion conductor.
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Affiliation(s)
- Sergey N Marshenya
- Center for Energy Science and Technology, Skolkovo Institute of Science and Technology, 3 Nobel Street, 121205 Moscow, Russia.
| | - Artem D Dembitskiy
- Center for Energy Science and Technology, Skolkovo Institute of Science and Technology, 3 Nobel Street, 121205 Moscow, Russia.
| | - Dmitry S Fedorov
- Institute of Solid State Chemistry of the Ural Branch of the Russian Academy of Science, 91 Pervomaiskaya Street, 620990 Ekaterinburg, Russia
- M.N. Mikheev Institute of Metal Physics of Ural Branch of Russian Academy of Science, 18 S. Kovalevskaya Street, 620137 Ekaterinburg, Russia
| | - Alexey G Scherbakov
- Center for Energy Science and Technology, Skolkovo Institute of Science and Technology, 3 Nobel Street, 121205 Moscow, Russia.
| | - Ivan A Trussov
- Center for Energy Science and Technology, Skolkovo Institute of Science and Technology, 3 Nobel Street, 121205 Moscow, Russia.
| | - Olga Emelianova
- Center for Energy Science and Technology, Skolkovo Institute of Science and Technology, 3 Nobel Street, 121205 Moscow, Russia.
| | - Dmitry A Aksyonov
- Center for Energy Science and Technology, Skolkovo Institute of Science and Technology, 3 Nobel Street, 121205 Moscow, Russia.
| | - Anton L Buzlukov
- M.N. Mikheev Institute of Metal Physics of Ural Branch of Russian Academy of Science, 18 S. Kovalevskaya Street, 620137 Ekaterinburg, Russia
| | - Nikolai A Zhuravlev
- Institute of Solid State Chemistry of the Ural Branch of the Russian Academy of Science, 91 Pervomaiskaya Street, 620990 Ekaterinburg, Russia
| | - Tatiana A Denisova
- Institute of Solid State Chemistry of the Ural Branch of the Russian Academy of Science, 91 Pervomaiskaya Street, 620990 Ekaterinburg, Russia
| | - Nadezhda I Medvedeva
- Institute of Solid State Chemistry of the Ural Branch of the Russian Academy of Science, 91 Pervomaiskaya Street, 620990 Ekaterinburg, Russia
| | - Artem M Abakumov
- Center for Energy Science and Technology, Skolkovo Institute of Science and Technology, 3 Nobel Street, 121205 Moscow, Russia.
| | - Evgeny V Antipov
- Center for Energy Science and Technology, Skolkovo Institute of Science and Technology, 3 Nobel Street, 121205 Moscow, Russia.
- Department of Chemistry, Lomonosov Moscow State University, 119991 Moscow, Russia
| | - Stanislav S Fedotov
- Center for Energy Science and Technology, Skolkovo Institute of Science and Technology, 3 Nobel Street, 121205 Moscow, Russia.
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Hinz Y, Beerwerth J, Böhmer R. Anion dynamics and motional decoupling in a glycerol-choline chloride deep eutectic solvent studied by one- and two-dimensional 35Cl NMR. Phys Chem Chem Phys 2023; 25:28130-28140. [PMID: 37818622 DOI: 10.1039/d3cp03668e] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/12/2023]
Abstract
Chlorine-35 is among the few nuclides that provide an experimental handle on the anion dynamics in choline based deep eutectic solvents. By combining several nuclear magnetic resonance (NMR) techniques, the present work examines the Cl- motions within glyceline, a glycerol : choline chloride 2 : 1 solution, in a large temperature range down to the glass transition temperature Tg. The applied methods include spin relaxometry, second-order line shape analysis, as well as two-dimensional central-transition exchange and stimulated-echo spectroscopy. The finding of unstructured central-transition NMR spectra characterized by a relatively small average quadrupolar coupling attests to a highly disordered, essentially nondirectional anionic coordination in glyceline. For temperatures larger than about 1.3Tg the chlorine motions are well coupled to those of the glycerol and the choline moieties. At lower temperatures the local translational anion dynamics become Arrhenian and increasingly faster than the motion of glyceline's matrix molecules. Upon further cooling, the overall ionic conductivity continues to display a super-Arrhenius behavior, implying that the choline cations rather than the Cl anions dominate the long-range charge transport also near Tg.
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Affiliation(s)
- Yannik Hinz
- Fakultät Physik, Technische Universität Dortmund, 44221 Dortmund, Germany
| | - Joachim Beerwerth
- Fakultät Physik, Technische Universität Dortmund, 44221 Dortmund, Germany
| | - Roland Böhmer
- Fakultät Physik, Technische Universität Dortmund, 44221 Dortmund, Germany
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3
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Hoffmann L, Beerwerth J, Moch K, Böhmer R. Phenol, the simplest aromatic monohydroxy alcohol, displays a faint Debye-like process when mixed with a nonassociating liquid. Phys Chem Chem Phys 2023; 25:24042-24059. [PMID: 37654228 DOI: 10.1039/d3cp02774k] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/02/2023]
Abstract
Solvated in propylene carbonate, viscous phenol is studied using dielectric spectroscopy and shear rheology. In addition, several oxygen-17 and deuteron nuclear magnetic resonance (NMR) techniques are applied to specifically isotope labeled equimolar mixtures. Quantum chemical calculations are used to check the electrical field gradient at phenol's oxygen site. The chosen combination of NMR methods facilitates the selective examination of potentially hydrogen-bond related contributions as well as those dominated by the structural relaxation. Taken together the present results for phenol in equimolar mixtures with the van der Waals liquid propylene carbonate provide evidence for the existence of a very weak Debye-like process that originates from ringlike supramolecular associates.
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Affiliation(s)
- Lars Hoffmann
- Fakultät Physik, Technische Universität Dortmund, 44221 Dortmund, Germany
| | - Joachim Beerwerth
- Fakultät Physik, Technische Universität Dortmund, 44221 Dortmund, Germany
| | - Kevin Moch
- Fakultät Physik, Technische Universität Dortmund, 44221 Dortmund, Germany
| | - Roland Böhmer
- Fakultät Physik, Technische Universität Dortmund, 44221 Dortmund, Germany
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Wolf T, Eden-Kossoy A, Frydman L. Indirectly detected satellite-transition quadrupolar NMR via progressive saturation of the proton reservoir. SOLID STATE NUCLEAR MAGNETIC RESONANCE 2023; 125:101862. [PMID: 36989551 DOI: 10.1016/j.ssnmr.2023.101862] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/04/2023] [Revised: 03/08/2023] [Accepted: 03/12/2023] [Indexed: 06/11/2023]
Abstract
Static satellite-transitions (ST) NMR line shapes from half-integer quadrupolar nuclei could be very informative: they can deliver insight about local motions over a wide range of timescales, and can report on small changes in the local electronic environments as reflected by variations in the quadrupolar parameters. Satellite transitions, however, are typically "invisible" for half-integer quadrupolar nuclei due to their sheer breadth, leading to low signal-to-noise ratio -especially for unreceptive low-gamma or dilute quadrupolar nuclei. Very recently we have introduced a method for enhancing the NMR sensitivity of unreceptive X nuclei in static solids dubbed PROgressive Saturation of the Proton Reservoir (PROSPR), which opens the possibility of magnifying the signals from such spins by repeatedly imprinting frequency-selective X-driven depolarizations on the much more sensitive 1H NMR signal. Here, we show that PROSPR's efficacy is high enough for enabling the detection of static ST NMR for challenging species like 35Cl, 33S and even 17O -all at natural-abundance. The ensuing ST-PROSPR NMR experiment thus opens new approaches to probe ultra-wideline (6-8 MHz wide) spectra. These highly pronounced anisotropies can in turn deliver new vistas about dynamic changes in solids, as here illustrated by tracking ST line shapes as a function of temperature during thermally-driven events.
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Affiliation(s)
- Tamar Wolf
- Department of Chemical and Biological Physics, Weizmann Institute of Science, Rehovot, 7610001, Israel
| | - Anna Eden-Kossoy
- Department of Chemical Research Support, Weizmann Institute of Science, Rehovot, 7610001, Israel
| | - Lucio Frydman
- Department of Chemical and Biological Physics, Weizmann Institute of Science, Rehovot, 7610001, Israel.
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5
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Hoffmann L, Beerwerth J, Adjei-Körner M, Fuentes-Landete V, Tonauer CM, Loerting T, Böhmer R. Oxygen NMR of high-density and low-density amorphous ice. J Chem Phys 2022; 156:084503. [DOI: 10.1063/5.0080333] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Using oxygen-17 as a nuclear probe, spin relaxometry was applied to study the high-density and low-density states of amorphous ice, covering temperatures below and somewhat above their glass transitions. These findings are put in perspective with results from deuteron nuclear magnetic resonance and with calculations based on dielectrically detected correlation times. This comparison reveals the presence of a wide distribution of correlation times. Furthermore, oxygen-17 central-transition echo spectra were recorded for wide ranges of temperature and pulse spacing. The spectra cannot be described by a single set of quadrupolar parameters, suggesting a distribution of H–O–H opening angles that is broader for high-density than for low-density amorphous ice. Simulations of the pulse separation dependent spin-echo spectra for various scenarios demonstrate that a small-step frequency diffusion process, assigned to the presence of homonuclear oxygen–oxygen interactions, determines the shape evolution of the pulse-separation-dependent spectra.
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Affiliation(s)
- Lars Hoffmann
- Fakultät Physik, Technische Universität Dortmund, 44221 Dortmund, Germany
| | - Joachim Beerwerth
- Fakultät Physik, Technische Universität Dortmund, 44221 Dortmund, Germany
| | | | - Violeta Fuentes-Landete
- Institute of Physical Chemistry, University of Innsbruck, Innrain 52c, A-6020 Innsbruck, Austria
| | - Christina M. Tonauer
- Institute of Physical Chemistry, University of Innsbruck, Innrain 52c, A-6020 Innsbruck, Austria
| | - Thomas Loerting
- Institute of Physical Chemistry, University of Innsbruck, Innrain 52c, A-6020 Innsbruck, Austria
| | - Roland Böhmer
- Fakultät Physik, Technische Universität Dortmund, 44221 Dortmund, Germany
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6
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Bräuniger T, Bielec P, Zeman OEO, Moudrakovski IL, Hoch C, Schnick W. Synthesis of the scandium chloride hydrates ScCl3·3H2O and Sc2Cl4(OH)2·12H2O and their characterisation by X-ray diffraction, 45Sc NMR spectroscopy and DFT calculations. ZEITSCHRIFT FUR NATURFORSCHUNG SECTION B-A JOURNAL OF CHEMICAL SCIENCES 2021. [DOI: 10.1515/znb-2021-0009] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Abstract
Abstract
The compounds ScCl3·3H2O (SCTH) and [{Sc(H2O)5(μ-OH)}2]Cl4·2H2O (SCOH), have been synthesised and characterised by single-crystal XRD, 45Sc NMR spectroscopy and DFT calculations, with the crystal structure of SCTH reported here for the first time. From 45Sc NMR measurements under static and MAS conditions, both chemical shift and quadrupolar coupling parameters have been determined. The quadrupolar coupling constants χ for the octahedrally coordinated scandium sites in SCTH are 2.0 ± 0.1 MHz for Sc(1) and 3.81 ± 0.05 MHz for Sc(2). For SCOH, where the hepta-coordination of the single scandium site constitutes a less symmetric electronic environment, 14.68 ± 0.05 MHz was found. DFT calculations for the static SCTH structure consistently overestimate the quadrupolar coupling constants, indicating the possible presence of crystal water dynamics on the NMR time scale.
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Affiliation(s)
- Thomas Bräuniger
- Department of Chemistry , University of Munich (LMU) , Butenandtstr. 5–13, 81377 Munich , Germany
| | - Philipp Bielec
- Department of Chemistry , University of Munich (LMU) , Butenandtstr. 5–13, 81377 Munich , Germany
| | - Otto E. O. Zeman
- Department of Chemistry , University of Munich (LMU) , Butenandtstr. 5–13, 81377 Munich , Germany
| | - Igor L. Moudrakovski
- Max-Planck-Institute for Solid-State Research , Heisenbergstr. 1, 70569 Stuttgart , Germany
| | - Constantin Hoch
- Department of Chemistry , University of Munich (LMU) , Butenandtstr. 5–13, 81377 Munich , Germany
| | - Wolfgang Schnick
- Department of Chemistry , University of Munich (LMU) , Butenandtstr. 5–13, 81377 Munich , Germany
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Dai Y, Wu G. Solid-State 17O NMR Studies of Sulfonate Jump Dynamics in Crystalline Sulfonic Acids: Insights into the Hydrogen Bonding Effect. J Phys Chem A 2020; 124:9597-9604. [PMID: 33151689 DOI: 10.1021/acs.jpca.0c08198] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We report variable-temperature (VT) 17O solid-state nuclear magnetic resonance (NMR) spectra for three crystalline sulfonic acids: l-cysteic acid monohydrate (CA), 3-pyridinesulfonic acid (PSA), and p-toluenesulfonic acid monohydrate (TSA). We were able to analyze the experimental VT 17O NMR spectra to obtain the activation barriers for SO3- jumps in these systems. Using the density functional-based tight-binding (DFTB) method, we performed potential energy surface scans for SO3- jumps in the crystal lattice of CA, PSA, and TSA, as well as for three related crystalline sulfonic acids (taurine, homotaurine, and 4-aminobutane-1-sulfonic acid) for which relevant 17O solid-state NMR data are available in the literature. The calculated activation barriers are in reasonable agreement with the experimental values. On the basis of the DFTB results, we hypothesized that activation barriers for SO3- jumps in the crystal lattice depend largely on the hydrogen bonding energy difference between the ground state and the transition state.
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Affiliation(s)
- Yizhe Dai
- Department of Chemistry, Queen's University, 90 Bader Lane, Kingston, Ontario K7L 3N6, Canada
| | - Gang Wu
- Department of Chemistry, Queen's University, 90 Bader Lane, Kingston, Ontario K7L 3N6, Canada
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8
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Sen S. Dynamics in inorganic glass-forming liquids by NMR spectroscopy. PROGRESS IN NUCLEAR MAGNETIC RESONANCE SPECTROSCOPY 2020; 116:155-176. [PMID: 32130956 DOI: 10.1016/j.pnmrs.2019.11.001] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/26/2019] [Revised: 10/08/2019] [Accepted: 11/07/2019] [Indexed: 06/10/2023]
Abstract
Dynamical NMR spectroscopy provides unique mechanistic understanding of the transport and relaxation processes in glass-forming liquids over timescales typically ranging from ~10-9 s to ~102 s, and thus has been used extensively in the past to study the dynamical behavior of polymeric and organic glass-forming liquids. However, reports in the literature of similar studies on inorganic glass-forming liquids have remained somewhat limited due to the experimental challenges. In this contribution we present a review of the high-temperature NMR spectroscopic studies of atomic and molecular dynamics in a wide variety of inorganic glass-forming liquids including oxides, halides and chalcogenides as well as select ionic liquids and molten salts. The significance of these dynamical processes in understanding the nature of the liquid-to-glass transition and their connection with the macroscopic transport properties of these liquids are discussed.
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Affiliation(s)
- Sabyasachi Sen
- Department of Materials Science & Engineering, University of California at Davis, Davis, CA 95616, USA.
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9
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Hoffmann L, Beerwerth J, Greim D, Senker J, Sternemann C, Hiller W, Böhmer R. Reorientational dynamics of trimethoxyboroxine: A molecular glass former studied by dielectric spectroscopy and 11B nuclear magnetic resonance. J Chem Phys 2020; 152:034503. [PMID: 31968976 DOI: 10.1063/1.5129769] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In this work, trimethoxyboroxine (TMB) is identified as a small-molecule glass former. In its viscous liquid as well as glassy states, static and dynamic properties of TMB are explored using various techniques. It is found that, on average, the structure of the condensed TMB molecules deviates from threefold symmetry so that TMB's electric dipole moment is nonzero, thus rendering broadband dielectric spectroscopy applicable. This method reveals the super-Arrhenius dynamics that characterizes TMB above its glass transition, which occurs at about 204 K. To extend the temperature range in which the molecular dynamics can be studied, 11B nuclear magnetic resonance experiments are additionally carried out on rotating and stationary samples: Exploiting dynamic second-order shifts, spin-relaxation times, line shape effects, as well as stimulated-echo and two-dimensional exchange spectroscopy, a coherent picture regarding the dynamics of this glass former is gained.
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Affiliation(s)
- Lars Hoffmann
- Fakultät Physik, Technische Universität Dortmund, D-44221 Dortmund, Germany
| | - Joachim Beerwerth
- Fakultät Physik, Technische Universität Dortmund, D-44221 Dortmund, Germany
| | - Dominik Greim
- Anorganische Chemie III, Universität Bayreuth, D-95440 Bayreuth, Germany
| | - Jürgen Senker
- Anorganische Chemie III, Universität Bayreuth, D-95440 Bayreuth, Germany
| | - Christian Sternemann
- DELTA/Fakultät Physik, Technische Universität Dortmund, D-44221 Dortmund, Germany
| | - Wolf Hiller
- Fakultät für Chemie und Chemische Biologie, Technische Universität Dortmund, D-44221 Dortmund, Germany
| | - Roland Böhmer
- Fakultät Physik, Technische Universität Dortmund, D-44221 Dortmund, Germany
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10
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Wu G. 17O NMR studies of organic and biological molecules in aqueous solution and in the solid state. PROGRESS IN NUCLEAR MAGNETIC RESONANCE SPECTROSCOPY 2019; 114-115:135-191. [PMID: 31779879 DOI: 10.1016/j.pnmrs.2019.06.002] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/25/2019] [Revised: 06/11/2019] [Accepted: 06/11/2019] [Indexed: 06/10/2023]
Abstract
This review describes the latest developments in the field of 17O NMR spectroscopy of organic and biological molecules both in aqueous solution and in the solid state. In the first part of the review, a general theoretical description of the nuclear quadrupole relaxation process in isotropic liquids is presented at a mathematical level suitable for non-specialists. In addition to the first-order quadrupole interaction, the theory also includes additional relaxation mechanisms such as the second-order quadrupole interaction and its cross correlation with shielding anisotropy. This complete theoretical treatment allows one to assess the transverse relaxation rate (thus the line width) of NMR signals from half-integer quadrupolar nuclei in solution over the entire range of motion. On the basis of this theoretical framework, we discuss general features of quadrupole-central-transition (QCT) NMR, which is a particularly powerful method of studying biomolecules in the slow motion regime. Then we review recent advances in 17O QCT NMR studies of biological macromolecules in aqueous solution. The second part of the review is concerned with solid-state 17O NMR studies of organic and biological molecules. As a sequel to the previous review on the same subject [G. Wu, Prog. Nucl. Magn. Reson. Spectrosc. 52 (2008) 118-169], the current review provides a complete coverage of the literature published since 2008 in this area.
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Affiliation(s)
- Gang Wu
- Department of Chemistry, Queen's University, 90 Bader Lane, Kingston, Ontario K7L 3N6, Canada.
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Kipnusu WK, Elsayed M, Iacob C, Pawlus S, Krause-Rehberg R, Paluch M. Glassy dynamics predicted by mutual role of free and activation volumes. SOFT MATTER 2019; 15:4656-4661. [PMID: 31149697 DOI: 10.1039/c9sm00363k] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
Broadband Dielectric Spectroscopy (BDS) at elevated pressures and Positron Annihilation Lifetime Spectroscopy (PALS) are employed to elucidate the importance of the ratio of activation and free volumes during vitrification. We show that this ratio has a linear correlation with the structural relaxation of glass forming liquids in a wide temperature range hence engendering it as a vital input in the description of the dynamic glass transition.
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Affiliation(s)
- Wycliffe K Kipnusu
- GROC UJI, Institute of New Imaging Technologies, Department of Physics, Universitat Jaume I, Avda. Sos Baynat s/n, 12071 Castellón, Spain.
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12
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Beerwerth J, Bierwirth SP, Adam J, Gainaru C, Böhmer R. Local and global dynamics of the viscous ion conductors 2Ca(NO3)2-3KNO3 and 2Ca(NO3)2-3RbNO3 probed by 87Rb nuclear magnetic resonance and shear rheology. J Chem Phys 2019; 150:194503. [DOI: 10.1063/1.5093973] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Joachim Beerwerth
- Fakultät Physik, Technische Universität Dortmund, D-44221 Dortmund, Germany
| | - S. Peter Bierwirth
- Fakultät Physik, Technische Universität Dortmund, D-44221 Dortmund, Germany
| | - Jens Adam
- Fakultät Physik, Technische Universität Dortmund, D-44221 Dortmund, Germany
| | - Catalin Gainaru
- Fakultät Physik, Technische Universität Dortmund, D-44221 Dortmund, Germany
| | - Roland Böhmer
- Fakultät Physik, Technische Universität Dortmund, D-44221 Dortmund, Germany
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