1
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Medvedev IG. Classical master equations and broadened classical master equations: Some analytical results. J Chem Phys 2021; 155:114116. [PMID: 34551549 DOI: 10.1063/5.0064325] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Some analytical results for the steady-state properties of the single-molecule tunneling junction are obtained with the use of the broadened classical master equations and classical master equations. The case of the one electronic level of the bridge molecule coupled to a single classical harmonic oscillator is considered within the spin-less model. Based on these equations, we establish some relations between different average values of interest, considering the large bias limit and the limit of the weak electron-oscillator coupling. We derive the analytical expressions for a number of characteristic properties of the tunneling junction in these limiting cases, compare our results with those obtained by the numerically exact calculations, and find that our expressions work very well. In the diabatic regime, the approximate solutions of the classical master equations are suggested, which permit us to introduce the effective temperature Teff and perform rather simple calculations of the average vibrational excitations N and the tunnel current I. It is shown that in the adiabatic regime, the properties of the tunneling junction depend essentially on the effective temperature Teff ad. We obtain the analytical expressions for Teff ad using different approaches for the treatment of the adiabatic regime. For both the diabatic and adiabatic regimes, we calculate Teff, Teff ad, N, and I, compare our results with those available in the literature, and confirm well agreement. The dependence of N and I on the reorganization energy and the position of the electronic level of the bridge molecule is discussed.
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Affiliation(s)
- Igor G Medvedev
- A. N. Frumkin Institute of Physical Chemistry and Electrochemistry of Russian Academy of Sciences, Leninsky Prospect 31, 119071 Moscow, Russian Federation
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2
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Chalupa P, Schäfer T, Reitner M, Springer D, Andergassen S, Toschi A. Fingerprints of the Local Moment Formation and its Kondo Screening in the Generalized Susceptibilities of Many-Electron Problems. PHYSICAL REVIEW LETTERS 2021; 126:056403. [PMID: 33605751 DOI: 10.1103/physrevlett.126.056403] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/23/2020] [Revised: 12/08/2020] [Accepted: 01/08/2021] [Indexed: 06/12/2023]
Abstract
We identify the precise hallmarks of the local magnetic moment formation and its Kondo screening in the frequency structure of the generalized charge susceptibility. The sharpness of our identification even pinpoints an alternative criterion to determine the Kondo temperature of strongly correlated systems on the two-particle level, which only requires calculations at the lowest Matsubara frequency. We showcase its strength by applying it to the single impurity and the periodic Anderson model as well as to the Hubbard model. Our results represent a significant progress for the general understanding of quantum field theory at the two-particle level and allow for tracing the limits of the physics captured by perturbative approaches for correlated systems.
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Affiliation(s)
- P Chalupa
- Institute of Solid State Physics, TU Wien, A-1040 Vienna, Austria
| | - T Schäfer
- Collège de France, 11 place Marcelin Berthelot, 75005 Paris, France
- CPHT, CNRS, École Polytechnique, Institut Polytechnique de Paris, Route de Saclay, 91128 Palaiseau, France
| | - M Reitner
- Institute of Solid State Physics, TU Wien, A-1040 Vienna, Austria
| | - D Springer
- Institute of Solid State Physics, TU Wien, A-1040 Vienna, Austria
- Institute of Advanced Research in Artificial Intelligence, IARAI, A-1030 Vienna, Austria
| | - S Andergassen
- Institut für Theoretische Physik and Center for Quantum Science, Universität Tübingen, Auf der Morgenstelle 14, 72076 Tübingen, Germany
| | - A Toschi
- Institute of Solid State Physics, TU Wien, A-1040 Vienna, Austria
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3
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Cohen G, Galperin M. Green’s function methods for single molecule junctions. J Chem Phys 2020; 152:090901. [DOI: 10.1063/1.5145210] [Citation(s) in RCA: 25] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/12/2023] Open
Affiliation(s)
- Guy Cohen
- The Raymond and Beverley Sackler Center for Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv 69978, Israel
- School of Chemistry, Tel Aviv University, Tel Aviv 69978, Israel
| | - Michael Galperin
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, USA
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4
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Exact relations for the differential conductance and rectification ratio of the tunnel current in the redox-mediated tunneling junctions and demonstration within the fully diabatic approximation for electron transitions. J Electroanal Chem (Lausanne) 2020. [DOI: 10.1016/j.jelechem.2019.113640] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
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Reimer V, Wegewijs MR, Nestmann K, Pletyukhov M. Five approaches to exact open-system dynamics: Complete positivity, divisibility, and time-dependent observables. J Chem Phys 2019; 151:044101. [PMID: 31370525 DOI: 10.1063/1.5094412] [Citation(s) in RCA: 16] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
To extend the classical concept of Markovianity to an open quantum system, different notions of the divisibility of its dynamics have been introduced. Here, we analyze this issue by five complementary approaches: equations of motion, real-time diagrammatics, Kraus-operator sums, as well as time-local and nonlocal (Nakajima-Zwanzig) quantum master equations. As a case study featuring several types of divisible dynamics, we examine in detail an exactly solvable noninteracting fermionic resonant level coupled arbitrarily strongly to a fermionic bath at an arbitrary temperature in the wideband limit. In particular, the impact of divisibility on the time-dependence of the observable level occupation is investigated and compared with typical Markovian approximations. We find that the loss of semigroup-divisibility is accompanied by a prominent reentrant behavior: Counter to intuition, the level occupation may temporarily increase significantly in order to reach a stationary state with smaller occupation, implying a reversal of the measurable transport current. In contrast, the loss of the so-called completely positive divisibility is more subtly signaled by the prohibition of such current reversals in specific time-intervals. Experimentally, it can be detected in the family of transient currents obtained by varying the initial occupation. To quantify the nonzero footprint left by the system in its effective environment, we determine the exact time-dependent state of the latter as well as related information measures such as entropy, exchange entropy, and coherent information.
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Affiliation(s)
- V Reimer
- Institute for Theory of Statistical Physics, RWTH Aachen, Aachen, Germany
| | - M R Wegewijs
- Institute for Theory of Statistical Physics, RWTH Aachen, Aachen, Germany
| | - K Nestmann
- Institute for Theory of Statistical Physics, RWTH Aachen, Aachen, Germany
| | - M Pletyukhov
- Institute for Theory of Statistical Physics, RWTH Aachen, Aachen, Germany
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6
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Seo M, Roulleau P, Roche P, Glattli DC, Sanquer M, Jehl X, Hutin L, Barraud S, Parmentier FD. Strongly Correlated Charge Transport in Silicon Metal-Oxide-Semiconductor Field-Effect Transistor Quantum Dots. PHYSICAL REVIEW LETTERS 2018; 121:027701. [PMID: 30085716 DOI: 10.1103/physrevlett.121.027701] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/22/2018] [Indexed: 06/08/2023]
Abstract
Quantum shot noise probes the dynamics of charge transfers through a quantum conductor, reflecting whether quasiparticles flow across the conductor in a steady stream, or in syncopated bursts. We have performed high-sensitivity shot noise measurements in a quantum dot obtained in a silicon metal-oxide-semiconductor field-effect transistor. The quality of our device allows us to precisely associate the different transport regimes and their statistics with the internal state of the quantum dot. In particular, we report on large current fluctuations in the inelastic cotunneling regime, corresponding to different highly correlated, non-Markovian charge transfer processes. We have also observed unusually large current fluctuations at low energy in the elastic cotunneling regime, the origin of which remains to be fully investigated.
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Affiliation(s)
- M Seo
- SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay, 91191 Gif-sur-Yvette cedex, France
| | - P Roulleau
- SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay, 91191 Gif-sur-Yvette cedex, France
| | - P Roche
- SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay, 91191 Gif-sur-Yvette cedex, France
| | - D C Glattli
- SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay, 91191 Gif-sur-Yvette cedex, France
| | - M Sanquer
- Université Grenoble Alpes, CEA, INAC-PHELIQS, 38000 Grenoble, France
| | - X Jehl
- Université Grenoble Alpes, CEA, INAC-PHELIQS, 38000 Grenoble, France
| | - L Hutin
- CEA, LETI, Minatec Campus, 38000 Grenoble, France
| | - S Barraud
- CEA, LETI, Minatec Campus, 38000 Grenoble, France
| | - F D Parmentier
- SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay, 91191 Gif-sur-Yvette cedex, France
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7
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Mejía L, Renaud N, Franco I. Signatures of Conformational Dynamics and Electrode-Molecule Interactions in the Conductance Profile During Pulling of Single-Molecule Junctions. J Phys Chem Lett 2018; 9:745-750. [PMID: 29369638 DOI: 10.1021/acs.jpclett.7b03323] [Citation(s) in RCA: 23] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
We demonstrate that conductance can act as a sensitive probe of conformational dynamics and electrode-molecule interactions during the equilibrium and nonequilibrium pulling of molecular junctions. To do so, we use a combination of classical molecular dynamics simulations and Landauer electron transport computations to investigate the conductance of a family of Au-alkanedithiol-Au junctions as they are mechanically elongated. The simulations show an overall decay of the conductance during pulling that is due to a decrease in the through-space electrode-molecule interactions, and that sensitivity depends on the electrode geometry. In addition, characteristic kinks induced by level alignment shifts (and to a lesser extent by quantum destructive interference) were also observed superimposed to the overall decay during pulling simulations. The latter effect depends on the variation of the molecular dihedral angles during pulling and therefore offers an efficient solution to experimentally monitor conformational dynamics at the single-molecule limit.
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Affiliation(s)
- Leopoldo Mejía
- Department of Chemistry, University of Rochester , Rochester, New York 14627-0216, United States
| | - Nicolas Renaud
- Netherlands eScience Center , Science Park 140 1098 XG Amsterdam, The Netherlands
| | - Ignacio Franco
- Department of Chemistry, University of Rochester , Rochester, New York 14627-0216, United States
- Department of Physics, University of Rochester , Rochester, New York 14627-0216, United States
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8
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Thoss M, Evers F. Perspective: Theory of quantum transport in molecular junctions. J Chem Phys 2018; 148:030901. [DOI: 10.1063/1.5003306] [Citation(s) in RCA: 105] [Impact Index Per Article: 17.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Michael Thoss
- Institute of Physics, University of Freiburg, Hermann-Herder-Str. 3, D-79104 Freiburg, Germany
| | - Ferdinand Evers
- Institute of Theoretical Physics, University of Regensburg, Universitätsstr. 31, D-93053 Regensburg, Germany
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9
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Hahn T, Ludwig T, Timm C, Kortus J. Electronic structure, transport, and collective effects in molecular layered systems. BEILSTEIN JOURNAL OF NANOTECHNOLOGY 2017; 8:2094-2105. [PMID: 29090111 PMCID: PMC5647717 DOI: 10.3762/bjnano.8.209] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 02/10/2017] [Accepted: 09/08/2017] [Indexed: 06/07/2023]
Abstract
The great potential of organic heterostructures for organic device applications is exemplified by the targeted engineering of the electronic properties of phthalocyanine-based systems. The transport properties of two different phthalocyanine systems, a pure copper phthalocyanine (CoPc) and a flourinated copper phthalocyanine-manganese phthalocyanine (F16CoPc/MnPc) heterostructure, are investigated by means of density functional theory (DFT) and the non-equilibrium Green's function (NEGF) approach. Furthermore, a master-equation-based approach is used to include electronic correlations beyond the mean-field-type approximation of DFT. We describe the essential theoretical tools to obtain the parameters needed for the master equation from DFT results. Finally, an interacting molecular monolayer is considered within a master-equation approach.
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Affiliation(s)
- Torsten Hahn
- Institute of Theoretical Physics, TU Freiberg, Leipziger Str. 23, D-09599 Freiberg, Germany
| | - Tim Ludwig
- Institute of Theoretical Physics, Technische Universität Dresden, 01062 Dresden, Germany
| | - Carsten Timm
- Institute of Theoretical Physics, Technische Universität Dresden, 01062 Dresden, Germany
| | - Jens Kortus
- Institute of Theoretical Physics, TU Freiberg, Leipziger Str. 23, D-09599 Freiberg, Germany
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Gaudenzi R, Misiorny M, Burzurí E, Wegewijs MR, van der Zant HSJ. Transport mirages in single-molecule devices. J Chem Phys 2017. [DOI: 10.1063/1.4975767] [Citation(s) in RCA: 24] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022] Open
Affiliation(s)
- R. Gaudenzi
- Kavli Institute of Nanoscience, Delft University of Technology, 2600 GA Delft, The Netherlands
| | - M. Misiorny
- Department of Microtechnology and Nanoscience MC2, Chalmers University of Technology, 412 96 Göteborg, Sweden
- Faculty of Physics, Adam Mickiewicz University, 61-614 Poznań, Poland
| | - E. Burzurí
- Kavli Institute of Nanoscience, Delft University of Technology, 2600 GA Delft, The Netherlands
| | - M. R. Wegewijs
- Peter Grünberg Institut, Forschungszentrum Jülich, 52425 Jülich, Germany
- JARA-FIT, 52056 Aachen, Germany
- Institute for Theory of Statistical Physics, RWTH Aachen, 52056 Aachen, Germany
| | - H. S. J. van der Zant
- Kavli Institute of Nanoscience, Delft University of Technology, 2600 GA Delft, The Netherlands
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11
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Monakhov K, Moors M, Kögerler P. Perspectives for Polyoxometalates in Single-Molecule Electronics and Spintronics. ADVANCES IN INORGANIC CHEMISTRY 2017. [DOI: 10.1016/bs.adioch.2016.12.009] [Citation(s) in RCA: 30] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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12
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Büsser CA, Heidrich-Meisner F. Inducing spin correlations and entanglement in a double quantum dot through nonequilibrium transport. PHYSICAL REVIEW LETTERS 2013; 111:246807. [PMID: 24483691 DOI: 10.1103/physrevlett.111.246807] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/15/2013] [Indexed: 06/03/2023]
Abstract
For a double quantum dot system in a parallel geometry, we demonstrate that by combining the effects of a flux and driving an electrical current through the structure, the spin correlations between electrons localized in the dots can be controlled at will. In particular, a current can induce spin correlations even if the spins are uncorrelated in the initial equilibrium state. Therefore, we are able to engineer an entangled state in this double-dot structure. We take many-body correlations fully into account by simulating the real-time dynamics using the time-dependent density matrix renormalization group method. Using a canonical transformation, we provide an intuitive explanation for our results, related to Ruderman-Kittel-Kasuya-Yoshida physics driven by the bias.
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Affiliation(s)
- C A Büsser
- Department of Physics and Arnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilians-University Munich, 80333 Munich, Germany
| | - F Heidrich-Meisner
- Department of Physics and Arnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilians-University Munich, 80333 Munich, Germany and Institute for Theoretical Physics II, Friedrich-Alexander University Erlangen-Nuremberg, 91058 Erlangen, Germany
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Bai L, Zhang R, Duan CL. Tunable spin-dependent Andreev reflection in a four-terminal Aharonov-Bohm interferometer with coherent indirect coupling and Rashba spin-orbit interaction. NANOSCALE RESEARCH LETTERS 2012; 7:670. [PMID: 23228047 PMCID: PMC3575254 DOI: 10.1186/1556-276x-7-670] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 06/14/2012] [Accepted: 11/21/2012] [Indexed: 06/01/2023]
Abstract
: Using the nonequilibrium Green's function method, we theoretically study the Andreev reflection(AR) in a four-terminal Aharonov-Bohm interferometer containing a coupled double quantum dot with the Rashba spin-orbit interaction (RSOI) and the coherent indirect coupling via two ferromagnetic leads. When two ferromagnetic electrodes are in the parallel configuration, the spin-up conductance is equal to the spin-down conductance due to the absence of the RSOI. However, for the antiparallel alignment, the spin-polarized AR occurs resulting from the crossed AR (CAR) and the RSOI. The effects of the coherent indirect coupling, RSOI, and magnetic flux on the Andreev-reflected tunneling magnetoresistance are analyzed at length. The spin-related current is calculated, and a distinct swap effect emerges. Furthermore, the pure spin current can be generated due to the CAR when two ferromagnets become two half metals. It is found that the strong RSOI and the large indirect coupling are in favor of the CAR and the production of the strong spin current. The properties of the spin-related current are tunable in terms of the external parameters. Our results offer new ways to manipulate the spin-dependent transport.
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Affiliation(s)
- Long Bai
- College of Science, China University of Mining and Technology, Xuzhou, 221116, China
| | - Rong Zhang
- College of Science, China University of Mining and Technology, Xuzhou, 221116, China
| | - Chen-Long Duan
- School of Chemical Engineering and Technology, China University of Mining and Technology, Xuzhou, 221116, China
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Pletyukhov M, Schoeller H. Nonequilibrium Kondo model: crossover from weak to strong coupling. PHYSICAL REVIEW LETTERS 2012; 108:260601. [PMID: 23004950 DOI: 10.1103/physrevlett.108.260601] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/01/2012] [Indexed: 06/01/2023]
Abstract
We analyze the nonequilibrium Kondo model at finite voltage and temperature by using a new formulation of the real-time renormalization group method with the Laplace variable as the flow parameter. We evaluate the energy-dependent spin relaxation rate and nonlinear conductance, and derive an approximate form for the universal line shape for the latter in the whole crossover regime from weak to strong coupling. The results are shown to agree well with exact methods in equilibrium, Fermi-liquid theory, weak-coupling expansions, and recent experiments. For the transient spin dynamics we find a universal exponential decay in the long-time limit along with a truncation-dependent pre-exponential power law. For multichannel models a pure power-law decay typical for non-Fermi-liquid behavior is predicted.
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Affiliation(s)
- Mikhail Pletyukhov
- Institut für Theorie der Statistischen Physik, RWTH Aachen, 52056 Aachen, Germany.
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Crivillers N, Mas-Torrent M, Rovira C, Veciana J. Charge transport through unpaired spin-containing molecules on surfaces. ACTA ACUST UNITED AC 2012. [DOI: 10.1039/c2jm31164j] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/30/2023]
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17
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Lamba V, Wilkinson SJ, Arora C. Designing molecular devices by altering bond lengths. J Mol Model 2011; 17:3251-5. [DOI: 10.1007/s00894-011-1013-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/26/2010] [Accepted: 02/07/2011] [Indexed: 10/18/2022]
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Peralta-Videa JR, Zhao L, Lopez-Moreno ML, de la Rosa G, Hong J, Gardea-Torresdey JL. Nanomaterials and the environment: a review for the biennium 2008-2010. JOURNAL OF HAZARDOUS MATERIALS 2011; 186:1-15. [PMID: 21134718 DOI: 10.1016/j.jhazmat.2010.11.020] [Citation(s) in RCA: 274] [Impact Index Per Article: 21.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/21/2010] [Accepted: 11/04/2010] [Indexed: 05/20/2023]
Abstract
Applications of nanotechnology are touching almost every aspect of modern life. The increased use of engineered nanomaterials (ENMs) in consumer products, chemical and medical equipment, information technology, and energy, among others, has increased the number of publications (informative and scientific) on ENMs. By the 1950s, very few papers were committed to nanomaterials (NMs), but in 2009, more than 80,000 journal articles included the concept nanotechnology. The objective of this review is to compile and analyze publications on NMs in the biennium 2008-2010. This review includes the most recent publications in risk assessment/toxicity, characterization and stability, toxicity, fate and transport of NMs in terrestrial ecosystems, and new ENMs. Carbon nanotubes, metallic, metal oxides and hydroxides nanoparticles, quantum dots, and polystyrene NPs are included.
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Affiliation(s)
- Jose R Peralta-Videa
- Department of Chemistry, The University of Texas at El Paso, El Paso, TX 79968, USA
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