1
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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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2
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Reuhl M, Monnard P, Vogel M. Effects of partial crystallization on the glassy slowdown of aqueous ethylene glycol solutions. J Chem Phys 2021; 155:224501. [PMID: 34911309 DOI: 10.1063/5.0075457] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Combining differential scanning calorimetry, nuclear magnetic resonance, and broadband dielectric spectroscopy studies, we ascertain the glass transition of aqueous ethylene glycol (EG) solutions, in particular the effects of partial crystallization on their glassy slowdown. For the completely liquid solutions in the weakly supercooled regime, it is found that the dynamics of the components occur on very similar time scales, rotational and translational motions are coupled, and the structural (α) relaxation monotonously slows down with increasing EG concentration. Upon cooling, partial crystallization strongly alters the glassy dynamics of EG-poor solutions; in particular, it strongly retards the α relaxation of the remaining liquid fraction, causing a non-monotonous concentration dependence, and it results in a crossover from non-Arrhenius to Arrhenius temperature dependence. In the deeply supercooled regime, a recrossing of the respective α-relaxation times results from the Arrhenius behaviors of the partially frozen EG-poor solutions together with the non-Arrhenius behavior of the fully liquid EG-rich solutions. Exploiting the isotope selectivity of nuclear magnetic resonance, we observe different rotational dynamics of the components in this low-temperature range and determine the respective contributions to the ν relaxation decoupling from the α relaxation when the glass transition is approached. The results suggest that the ν process, which is usually regarded as a water process, actually also involves the EG molecules. In addition, we show that various kinds of partially crystalline aqueous systems share a common relaxation process, which is associated with the frozen fraction and differs from that of bulk hexagonal ice.
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Affiliation(s)
- Melanie Reuhl
- Institute for Condensed Matter Physics, Technische Universität Darmstadt, Hochschulstr. 6, 64289 Darmstadt, Germany
| | - Philipp Monnard
- Institute for Condensed Matter Physics, Technische Universität Darmstadt, Hochschulstr. 6, 64289 Darmstadt, Germany
| | - Michael Vogel
- Institute for Condensed Matter Physics, Technische Universität Darmstadt, Hochschulstr. 6, 64289 Darmstadt, Germany
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3
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Gallo P, Bachler J, Bove LE, Böhmer R, Camisasca G, Coronas LE, Corti HR, de Almeida Ribeiro I, de Koning M, Franzese G, Fuentes-Landete V, Gainaru C, Loerting T, de Oca JMM, Poole PH, Rovere M, Sciortino F, Tonauer CM, Appignanesi GA. Advances in the study of supercooled water. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2021; 44:143. [PMID: 34825973 DOI: 10.1140/epje/s10189-021-00139-1] [Citation(s) in RCA: 34] [Impact Index Per Article: 11.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/14/2021] [Accepted: 10/17/2021] [Indexed: 06/13/2023]
Abstract
In this review, we report recent progress in the field of supercooled water. Due to its uniqueness, water presents numerous anomalies with respect to most simple liquids, showing polyamorphism both in the liquid and in the glassy state. We first describe the thermodynamic scenarios hypothesized for the supercooled region and in particular among them the liquid-liquid critical point scenario that has so far received more experimental evidence. We then review the most recent structural indicators, the two-state model picture of water, and the importance of cooperative effects related to the fact that water is a hydrogen-bonded network liquid. We show throughout the review that water's peculiar properties come into play also when water is in solution, confined, and close to biological molecules. Concerning dynamics, upon mild supercooling water behaves as a fragile glass former following the mode coupling theory, and it turns into a strong glass former upon further cooling. Connections between the slow dynamics and the thermodynamics are discussed. The translational relaxation times of density fluctuations show in fact the fragile-to-strong crossover connected to the thermodynamics arising from the existence of two liquids. When considering also rotations, additional crossovers come to play. Mobility-viscosity decoupling is also discussed in supercooled water and aqueous solutions. Finally, the polyamorphism of glassy water is considered through experimental and simulation results both in bulk and in salty aqueous solutions. Grains and grain boundaries are also discussed.
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Affiliation(s)
- Paola Gallo
- Dipartimento di Matematica e Fisica, Università degli Studi Roma Tre, Via della Vasca Navale 84, 00146, Roma, Italy.
| | - Johannes Bachler
- Institute of Physical Chemistry, University of Innsbruck, Innrain 52c, A-6020, Innsbruck, Austria
| | - Livia E Bove
- Dipartimento di Fisica, Sapienza Università di Roma, Piazzale A. Moro 5, 00185, Roma, Italy
- Sorbonne Université, CNRS UMR 7590, IMPMC, 75005, Paris, France
| | - Roland Böhmer
- Fakultät Physik, Technische Universität Dortmund, 44221, Dortmund, Germany
| | - Gaia Camisasca
- Dipartimento di Matematica e Fisica, Università degli Studi Roma Tre, Via della Vasca Navale 84, 00146, Roma, Italy
| | - Luis E Coronas
- Secció de Física Estadística i Interdisciplinària-Departament de Física de la Matèria Condensada, Universitat de Barcelona, & Institut de Nanociència i Nanotecnologia (IN2UB), Universitat de Barcelona, C. Martí i Franquès 1, 08028, Barcelona, Spain
| | - Horacio R Corti
- Departamento de Física de la Materia Condensada, Centro Atómico Constituyentes, Comisión Nacional de Energía Atómica, B1650LWP, Buenos Aires, Argentina
| | - Ingrid de Almeida Ribeiro
- Instituto de Física "Gleb Wataghin", Universidade Estadual de Campinas, UNICAMP, 13083-859, Campinas, São Paulo, Brazil
| | - Maurice de Koning
- Instituto de Física "Gleb Wataghin", Universidade Estadual de Campinas, UNICAMP, 13083-859, Campinas, São Paulo, Brazil
- Center for Computing in Engineering & Sciences, Universidade Estadual de Campinas, UNICAMP, 13083-861, Campinas, São Paulo, Brazil
| | - Giancarlo Franzese
- Secció de Física Estadística i Interdisciplinària-Departament de Física de la Matèria Condensada, Universitat de Barcelona, & Institut de Nanociència i Nanotecnologia (IN2UB), Universitat de Barcelona, C. Martí i Franquès 1, 08028, Barcelona, Spain
| | - Violeta Fuentes-Landete
- Institute of Physical Chemistry, University of Innsbruck, Innrain 52c, A-6020, Innsbruck, Austria
| | - Catalin Gainaru
- Fakultät Physik, Technische Universität Dortmund, 44221, Dortmund, Germany
| | - Thomas Loerting
- Institute of Physical Chemistry, University of Innsbruck, Innrain 52c, A-6020, Innsbruck, Austria
| | | | - Peter H Poole
- Department of Physics, St. Francis Xavier University, Antigonish, NS, B2G 2W5, Canada
| | - Mauro Rovere
- Dipartimento di Matematica e Fisica, Università degli Studi Roma Tre, Via della Vasca Navale 84, 00146, Roma, Italy
| | - Francesco Sciortino
- Dipartimento di Fisica, Sapienza Università di Roma, Piazzale A. Moro 5, 00185, Roma, Italy
| | - Christina M Tonauer
- Institute of Physical Chemistry, University of Innsbruck, Innrain 52c, A-6020, Innsbruck, Austria
| | - Gustavo A Appignanesi
- INQUISUR, Departamento de Química, Universidad Nacional del Sur (UNS)-CONICET, Avenida Alem 1253, 8000, Bahía Blanca, Argentina
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4
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Steinrücken E, Wissel T, Brodrecht M, Breitzke H, Regentin J, Buntkowsky G, Vogel M. 2H NMR study on temperature-dependent water dynamics in amino-acid functionalized silica nanopores. J Chem Phys 2021; 154:114702. [PMID: 33752372 DOI: 10.1063/5.0044141] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We prepare various amino-acid functionalized silica pores with diameters of ∼6 nm and study the temperature-dependent reorientation dynamics of water in these confinements. Specifically, we link basic Lys, neutral Ala, and acidic Glu to the inner surfaces and combine 2H nuclear magnetic resonance spin-lattice relaxation and line shape analyses to disentangle the rotational motions of the surfaces groups and the crystalline and liquid water fractions coexisting below partial freezing. Unlike the crystalline phase, the liquid phase shows reorientation dynamics, which strongly depends on the chemistry of the inner surfaces. The water reorientation is slowest for the Lys functionalization, followed by Ala and Glu and, finally, the native silica pores. In total, the rotational correlation times of water at the different surfaces vary by about two orders of magnitude, where this span is largely independent of the temperature in the range ∼200-250 K.
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Affiliation(s)
- Elisa Steinrücken
- Institute for Condensed Matter Physics, Technische Universität Darmstadt, Hochschulstr. 6, 64289 Darmstadt, Germany
| | - Till Wissel
- Eduard-Zintl-Institut für Anorganische und Physikalische Chemie, Technische Universität Darmstadt, Alarich-Weiss-Str. 8, 64287 Darmstadt, Germany
| | - Martin Brodrecht
- Eduard-Zintl-Institut für Anorganische und Physikalische Chemie, Technische Universität Darmstadt, Alarich-Weiss-Str. 8, 64287 Darmstadt, Germany
| | - Hergen Breitzke
- Eduard-Zintl-Institut für Anorganische und Physikalische Chemie, Technische Universität Darmstadt, Alarich-Weiss-Str. 8, 64287 Darmstadt, Germany
| | - Julia Regentin
- Institute for Condensed Matter Physics, Technische Universität Darmstadt, Hochschulstr. 6, 64289 Darmstadt, Germany
| | - Gerd Buntkowsky
- Eduard-Zintl-Institut für Anorganische und Physikalische Chemie, Technische Universität Darmstadt, Alarich-Weiss-Str. 8, 64287 Darmstadt, Germany
| | - Michael Vogel
- Institute for Condensed Matter Physics, Technische Universität Darmstadt, Hochschulstr. 6, 64289 Darmstadt, Germany
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5
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Plaga LJ, Raidt A, Fuentes Landete V, Amann-Winkel K, Massani B, Gasser TM, Gainaru C, Loerting T, Böhmer R. Amorphous and crystalline ices studied by dielectric spectroscopy. J Chem Phys 2019; 150:244501. [DOI: 10.1063/1.5100785] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- L. J. Plaga
- Fakultät Physik, Technische Universität Dortmund, D-44221 Dortmund, Germany
| | - A. Raidt
- Fakultät Physik, Technische Universität Dortmund, D-44221 Dortmund, Germany
| | - V. Fuentes Landete
- Institute of Physical Chemistry, University of Innsbruck, A-6020 Innsbruck, Austria
| | - K. Amann-Winkel
- Institute of Physical Chemistry, University of Innsbruck, A-6020 Innsbruck, Austria
| | - B. Massani
- Institute of Physical Chemistry, University of Innsbruck, A-6020 Innsbruck, Austria
| | - T. M. Gasser
- Institute of Physical Chemistry, University of Innsbruck, A-6020 Innsbruck, Austria
| | - C. Gainaru
- Fakultät Physik, Technische Universität Dortmund, D-44221 Dortmund, Germany
| | - T. Loerting
- Institute of Physical Chemistry, University of Innsbruck, A-6020 Innsbruck, Austria
| | - R. Böhmer
- Fakultät Physik, Technische Universität Dortmund, D-44221 Dortmund, Germany
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6
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Yao Y, Fella V, Huang W, Zhang KAI, Landfester K, Butt HJ, Vogel M, Floudas G. Crystallization and Dynamics of Water Confined in Model Mesoporous Silica Particles: Two Ice Nuclei and Two Fractions of Water. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2019; 35:5890-5901. [PMID: 30946592 DOI: 10.1021/acs.langmuir.9b00496] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
The crystallization and dynamics of water confined in model mesoporous silica particles (pore diameters ranging from 2.1 to 5 nm; pore length ≈ 1 μm) are studied in homogeneous aqueous suspensions by dielectric spectroscopy, differential scanning calorimetry, and nuclear magnetic resonance (NMR) techniques. We establish the phase diagram ( T vs 1/ d) of confined water covering a broad range of pore diameters. A linear dependence of the heterogeneous and the homogeneous nucleation temperatures on the inverse pore diameter is shown. The two lines converge at a pore diameter of ∼2.6 nm, below which formation of stable crystals is suppressed. By combining dielectric spectroscopy and different NMR techniques, we determine the dynamics of water within mesoporous silica over broad temperature and frequency ranges. Both techniques identify two dynamically distinguishable fractions of confined water coexisting within the pores. We attribute the two fractions to an interfacial water layer at the pore walls and confined water in the pore interior. Two alternative scenarios are proposed to rationalize the coexistence of two dynamically distinguishable water fractions. In the first scenario, two liquid fractions of water coexist under extreme confinement conditions for a range of temperatures; we discuss similarities with the two ultraviscous liquids (high-density liquid and low-density liquid) put forward for supercooled bulk water. In the second scenario, a liquid and a solid phase coexist; we conjecture that highly distorted and unstable crystal nuclei exist under extreme confinement that exhibit reorientation dynamics with time scales intermediate to the surrounding confined liquid and to bulk ice.
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Affiliation(s)
- Yang Yao
- Max Planck Institute for Polymer Research , D-55128 Mainz , Germany
| | - Verena Fella
- Institut für Festkörperphysik , Technische Universität Darmstadt , Hochschulstraße 6 , 64289 Darmstadt , Germany
| | - Wei Huang
- Max Planck Institute for Polymer Research , D-55128 Mainz , Germany
| | - Kai A I Zhang
- Max Planck Institute for Polymer Research , D-55128 Mainz , Germany
| | | | - Hans-Jürgen Butt
- Max Planck Institute for Polymer Research , D-55128 Mainz , Germany
| | - Michael Vogel
- Institut für Festkörperphysik , Technische Universität Darmstadt , Hochschulstraße 6 , 64289 Darmstadt , Germany
| | - George Floudas
- Max Planck Institute for Polymer Research , D-55128 Mainz , Germany
- Department of Physics , University of Ioannina , P.O. Box 1186, 451 10 Ioannina , Greece
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7
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Weigler M, Brodrecht M, Buntkowsky G, Vogel M. Reorientation of Deeply Cooled Water in Mesoporous Silica: NMR Studies of the Pore-Size Dependence. J Phys Chem B 2019; 123:2123-2134. [DOI: 10.1021/acs.jpcb.8b12204] [Citation(s) in RCA: 32] [Impact Index Per Article: 6.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- M. Weigler
- Institut für Festkörperphysik, Technische Universität Darmstadt, Hochschulstr. 6, 64289 Darmstadt, Germany
| | - M. Brodrecht
- Eduard-Zintl-Institut für Anorganische und Physikalische Chemie, Technische Universität Darmstadt, Alarich-Weiss-Str. 8, 64287 Darmstadt, Germany
| | - G. Buntkowsky
- Eduard-Zintl-Institut für Anorganische und Physikalische Chemie, Technische Universität Darmstadt, Alarich-Weiss-Str. 8, 64287 Darmstadt, Germany
| | - M. Vogel
- Institut für Festkörperphysik, Technische Universität Darmstadt, Hochschulstr. 6, 64289 Darmstadt, Germany
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8
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Swenson J. Possible relations between supercooled and glassy confined water and amorphous bulk ice. Phys Chem Chem Phys 2018; 20:30095-30103. [DOI: 10.1039/c8cp05688a] [Citation(s) in RCA: 25] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/25/2023]
Abstract
A proposed relaxation scenario of bulk water based on studies of confined water and low density amorphous ice.
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Affiliation(s)
- Jan Swenson
- Department of Physics, Chalmers University of Technology
- SE-412 96 Göteborg
- Sweden
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9
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Parmentier A, Shephard JJ, Romanelli G, Senesi R, Salzmann CG, Andreani C. Evolution of Hydrogen Dynamics in Amorphous Ice with Density. J Phys Chem Lett 2015; 6:2038-2042. [PMID: 26266499 DOI: 10.1021/acs.jpclett.5b00711] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
The single-particle dynamics of hydrogen atoms in several of the amorphous ices are reported using a combination of deep inelastic neutron scattering (DINS) and inelastic neutron scattering (INS). The mean kinetic energies of the hydrogen nuclei are found to increase with increasing density, indicating the weakening of hydrogen bonds as well as a trend toward steeper and more harmonic hydrogen vibrational potential energy surfaces. DINS shows much more pronounced changes in the O-H stretching component of the mean kinetic energy going from low- to high-density amorphous ices than indicated by INS and Raman spectroscopy. This highlights the power of the DINS technique to retrieve accurate ground-state kinetic energies beyond the harmonic approximation. In a novel approach, we use information from DINS and INS to determine the anharmonicity constants of the O-H stretching modes. Furthermore, our experimental kinetic energies will serve as important benchmark values for path-integral Monte Carlo simulations.
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Affiliation(s)
- A Parmentier
- †Dipartimento di Fisica and NAST Centre, Università degli Studi di Roma Tor Vergata, Via della Ricerca Scientifica 1, 00133 Roma, Italy
| | - J J Shephard
- ‡Department of Chemistry, University College London, 20 Gordon Street, London WC1H 0AJ, United Kingdom
- §Department of Chemistry, Durham University, South Road, Durham DH1 3LE, United Kingdom
| | - G Romanelli
- †Dipartimento di Fisica and NAST Centre, Università degli Studi di Roma Tor Vergata, Via della Ricerca Scientifica 1, 00133 Roma, Italy
| | - R Senesi
- †Dipartimento di Fisica and NAST Centre, Università degli Studi di Roma Tor Vergata, Via della Ricerca Scientifica 1, 00133 Roma, Italy
- ∥CNR-IPCF Sezione di Messina, Viale F. Stagno D'Alcontres 37, 98158 Messina, Italy
| | - C G Salzmann
- ‡Department of Chemistry, University College London, 20 Gordon Street, London WC1H 0AJ, United Kingdom
| | - C Andreani
- †Dipartimento di Fisica and NAST Centre, Università degli Studi di Roma Tor Vergata, Via della Ricerca Scientifica 1, 00133 Roma, Italy
- ∥CNR-IPCF Sezione di Messina, Viale F. Stagno D'Alcontres 37, 98158 Messina, Italy
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10
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Costa P, Fernandez-Oliva M, Sanchez-Garcia E, Sander W. The highly reactive benzhydryl cation isolated and stabilized in water ice. J Am Chem Soc 2014; 136:15625-30. [PMID: 25236711 DOI: 10.1021/ja507894x] [Citation(s) in RCA: 27] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022]
Abstract
Diphenylcarbene (DPC) shows a triplet ground-state lying approximately 3 kcal/mol below the lowest singlet state. Under the conditions of matrix isolation at 25 K, DPC reacts with single water molecules embedded in solid argon and switches its ground state from triplet to singlet by forming a strong hydrogen bond. The complex between DPC and water is only metastable, and even at 3 K the carbene center slowly inserts into the OH bond of water to form benzhydryl alcohol via quantum chemical tunneling. Surprisingly, if DPC is generated in amorphous water ice at 3 K, it is protonated instantaneously to give the benzhydryl cation. Under these conditions, the benzhydryl cation is stable, and warming to temperatures above 50 K is required to produce benzhydryl alcohol. Thus, for the first time, a highly electrophilic and extremely reactive secondary carbenium ion can be isolated in a neutral, nucleophilic environment avoiding superacidic conditions.
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Affiliation(s)
- Paolo Costa
- Lehrstuhl für Organische Chemie II, Ruhr-Universität Bochum , 44780 Bochum, Germany
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11
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Sattig M, Reutter S, Fujara F, Werner M, Buntkowsky G, Vogel M. NMR studies on the temperature-dependent dynamics of confined water. Phys Chem Chem Phys 2014; 16:19229-40. [DOI: 10.1039/c4cp02057j] [Citation(s) in RCA: 52] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
NMR studies of water in nanoscopic confinements of various sizes reveal two dynamical crossovers related to a partial solidification of internal molecules and a glass transition of interfacial molecules, respectively.
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Affiliation(s)
- Matthias Sattig
- Institut für Festkörperphysik
- Technische Universität Darmstadt
- 64289 Darmstadt, Germany
| | - Stefan Reutter
- Institut für Festkörperphysik
- Technische Universität Darmstadt
- 64289 Darmstadt, Germany
| | - Franz Fujara
- Institut für Festkörperphysik
- Technische Universität Darmstadt
- 64289 Darmstadt, Germany
| | - Mayke Werner
- Eduard-Zintl-Institut für Anorganische und Physikalische Chemie
- Technische Universität Darmstadt
- 64287 Darmstadt, Germany
| | - Gerd Buntkowsky
- Eduard-Zintl-Institut für Anorganische und Physikalische Chemie
- Technische Universität Darmstadt
- 64287 Darmstadt, Germany
| | - Michael Vogel
- Institut für Festkörperphysik
- Technische Universität Darmstadt
- 64289 Darmstadt, Germany
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