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“Nonmonotonic field dependence of damping and reappearance of Rabi oscillations in quantum dots”. Vagov A, Croitoru MD, Axt VM, Kuhn T, Peeters FM, Physical review letters 98, 1 (2007). http://doi.org/10.1103/PhysRevLett.98.227403
Keywords: A1 Journal article; Condensed Matter Theory (CMT); Electron microscopy for materials research (EMAT)
Impact Factor: 8.462
Times cited: 91
DOI: 10.1103/PhysRevLett.98.227403
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“Quantum-size effects on T-c in superconducting nanofilms”. Shanenko AA, Croitoru MD, Peeters FM, Europhysics letters 76, 498 (2006). http://doi.org/10.1209/epl/i2006-10274-6
Keywords: A1 Journal article; Condensed Matter Theory (CMT); Electron microscopy for materials research (EMAT)
Impact Factor: 1.957
Times cited: 31
DOI: 10.1209/epl/i2006-10274-6
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“Shape resonances in the superconducting order parameter of ultrathin nanowires”. Shanenko AA, Croitoru MD, Physical review : B : condensed matter and materials physics 73, 012510 (2006). http://doi.org/10.1103/PhysRevB.73.012510
Keywords: A1 Journal article; Condensed Matter Theory (CMT); Electron microscopy for materials research (EMAT)
Impact Factor: 3.836
Times cited: 41
DOI: 10.1103/PhysRevB.73.012510
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“Size-dependent enhancement of superconductivity in Al and Sn nanowires: shape-resonance effect”. Shanenko AA, Croitoru MD, Zgirski M, Peeters FM, Arutyunov K, Physical review : B : condensed matter and materials physics 74, 052502 (2006). http://doi.org/10.1103/PhysRevB.74.052502
Keywords: A1 Journal article; Condensed Matter Theory (CMT); Electron microscopy for materials research (EMAT)
Impact Factor: 3.836
Times cited: 95
DOI: 10.1103/PhysRevB.74.052502
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“Superconducting nanofilms: Andreev-type states induced by quantum confinement”. Shanenko AA, Croitoru MD, Peeters FM, Physical review : B : solid state 78, 054505 (2008). http://doi.org/10.1103/PhysRevB.78.054505
Abstract: Quantum confinement of the transverse electron motion is the major effect governing the superconducting properties of high-quality metallic nanofilms, leading to a nonuniform transverse distribution of the superconducting condensate. In this case the order parameter can exhibit significant local enhancements due to these quantum-size effects and, consequently, quasiparticles have lower energies when they avoid the local enhancements of the pair condensate. Such excitations can be considered as new Andreev-type quasiparticles but now induced by quantum confinement. By numerically solving the Bogoliubovde Gennes equations and using Anderson's approximate solution to these equations, we: (a) formulate a criterion for such new Andreev-type states (NATS) and (b) study their effect on the superconducting characteristics in metallic nanofilms. We also argue that nanofilms made of low-carrier-density materials, e.g., of superconducting semiconductors, can be a more optimal choice for the observations of NATS and other quantum-size superconducting effects.
Keywords: A1 Journal article; Condensed Matter Theory (CMT); Electron microscopy for materials research (EMAT)
Impact Factor: 3.836
Times cited: 14
DOI: 10.1103/PhysRevB.78.054505
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“Superconducting nanowires: quantum-confinement effect on the critical magnetic field and supercurrent”. Croitoru MD, Shanenko AA, Peeters FM, International journal of modern physics: B: condensed matter physics, statistical physics, applied physics
T2 –, 32nd International Workshop on Condensed Matter Theories, Aug 12-19, 2008, Loughborough Univ, Loughborough, England 23, 4257 (2009). http://doi.org/10.1142/S0217979209063419
Abstract: We study the effect of electron confinement on the superconducting-to-normal phase transition driven by a magnetic field and/or on the current-carrying state of the superconducting condensate in nanowires. Our investigation is based on a self-consistent numerical solution of the Bogoliubov-de Gennes equations. We show that in a parallel magnetic field and/or in the presence of supercurrent the transition from superconducting to normal phase occurs as a cascade of discontinuous jumps in the superconducting order parameter for diameters D < 10 divided by 15 nm at T = 0. The critical magnetic field exhibits quantum-size oscillations with pronounced resonant enhancements.
Keywords: A1 Journal article; Condensed Matter Theory (CMT); Electron microscopy for materials research (EMAT)
Impact Factor: 0.736
Times cited: 1
DOI: 10.1142/S0217979209063419
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“Measurement of specimen thickness by phase change determination in TEM”. Croitoru MD, van Dyck D, Liu YZ, Zhang Z, Ultramicroscopy 108, 1616 (2008). http://doi.org/10.1016/j.ultramic.2008.06.002
Abstract: A non-destructive method for measuring the thickness of thin amorphous films composed of light elements has been developed. The method employs the statistics of the phase of the electron exit wave function. The accuracy of this method has been checked numerically by the multislice method and compared with that based on the mean inner potential.
Keywords: A1 Journal article; Condensed Matter Theory (CMT); Electron microscopy for materials research (EMAT); Vision lab
Impact Factor: 2.843
Times cited: 2
DOI: 10.1016/j.ultramic.2008.06.002
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“Statistical method for thickness measurement of amorphous objects”. van Dyck D, Croitoru MD, Applied physics letters 90, 241911 (2007). http://doi.org/10.1063/1.2749184
Abstract: The authors propose a nondestructive method for the determination of the thickness of an amorphous sample. This method is based on the statistics of the phase of the electron exit wave function, which depend on the number of atoms traversed by the incident electron which itself is a function of the thickness of the object. The accuracy of this method has been checked numerically by the multislice method and compared with that based on the mean inner potential. (c) 2007 American Institute of Physics.
Keywords: A1 Journal article; Condensed Matter Theory (CMT); Electron microscopy for materials research (EMAT); Vision lab
Impact Factor: 3.411
Times cited: 4
DOI: 10.1063/1.2749184
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“Diffusive transport in the hybrid Hall effect device”. Reijniers J, Peeters FM, Journal of applied physics 87, 8088 (2000). http://doi.org/10.1063/1.373502
Keywords: A1 Journal article; Condensed Matter Theory (CMT); Engineering Management (ENM)
Impact Factor: 2.068
Times cited: 12
DOI: 10.1063/1.373502
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“Electron scattering on circular symmetric magnetic profiles in a two-dimensional electron gas”. Reijniers J, Peeters FM, Matulis A, Physical review : B : condensed matter and materials physics 64, 245314 (2001). http://doi.org/10.1103/PhysRevB.64.245314
Keywords: A1 Journal article; Condensed Matter Theory (CMT); Engineering Management (ENM)
Impact Factor: 3.836
Times cited: 29
DOI: 10.1103/PhysRevB.64.245314
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“The Hall resistivity of a two-dimensional electron gas in the presence of magnetic clusters with perpendicular magnetization”. Reijniers J, Peeters FM, Matulis A, Physica. E: Low-dimensional systems and nanostructures 6, 759 (2000). http://doi.org/10.1016/S1386-9477(99)00197-6
Keywords: A1 Journal article; Condensed Matter Theory (CMT); Engineering Management (ENM)
Impact Factor: 2.221
Times cited: 9
DOI: 10.1016/S1386-9477(99)00197-6
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“Hybrid ferromagnetic/semiconductor Hall effect device”. Reijniers J, Peeters FM, Applied physics letters 73, 357 (1998). http://doi.org/10.1063/1.121833
Keywords: A1 Journal article; Condensed Matter Theory (CMT); Engineering Management (ENM)
Impact Factor: 3.411
Times cited: 35
DOI: 10.1063/1.121833
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“Quantum states in a magnetic anti-dot”. Reijniers J, Peeters FM, Matulis A, Physical review : B : condensed matter and materials physics 59, 2817 (1999). http://doi.org/10.1103/PhysRevB.59.2817
Keywords: A1 Journal article; Condensed Matter Theory (CMT); Engineering Management (ENM)
Impact Factor: 3.836
Times cited: 92
DOI: 10.1103/PhysRevB.59.2817
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“Resistance effects due to magnetic guiding orbits”. Reijniers J, Peeters FM, Physical review : B : condensed matter and materials physics 63, 165317 (2001). http://doi.org/10.1103/PhysRevB.63.165317
Keywords: A1 Journal article; Condensed Matter Theory (CMT); Engineering Management (ENM)
Impact Factor: 3.836
Times cited: 27
DOI: 10.1103/PhysRevB.63.165317
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“Snake orbits and related magnetic edge states”. Reijniers J, Peeters FM, Journal of physics : condensed matter 12, 9771 (2000). http://doi.org/10.1088/0953-8984/12/47/305
Keywords: A1 Journal article; Condensed Matter Theory (CMT); Engineering Management (ENM)
Impact Factor: 2.649
Times cited: 66
DOI: 10.1088/0953-8984/12/47/305
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“Snake orbits in hybrid semiconductor/ferromagnetic devices”. Peeters FM, Reijniers J, Badalian SM, Vasilopoulos P, Microelectronic engineering 47, 405 (1999). http://doi.org/10.1016/S0167-9317(99)00245-2
Keywords: A1 Journal article; Condensed Matter Theory (CMT); Engineering Management (ENM)
Impact Factor: 1.806
Times cited: 6
DOI: 10.1016/S0167-9317(99)00245-2
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“Structure and energetics of hydrogen chemisorbed on a single graphene layer to produce graphane”. Dzhurakhalov AA, Peeters FM, Carbon 49, 3258 (2011). http://doi.org/10.1016/j.carbon.2011.03.052
Abstract: Chemisorption of hydrogen on graphene is studied using atomistic simulations with the second generation of reactive empirical bond order Brenner inter-atomic potential. The lowest energy adsorption sites and the most important metastable sites are determined. The H concentration is varied from a single H atom, to clusters of H atoms up to full coverage. We found that when two or more H atoms are present, the most stable configurations of H chemisorption on a single graphene layer are ortho hydrogen pairs adsorbed on one side or on both sides of the graphene sheet. The latter has the highest hydrogen binding energy. The next stable configuration is the orthopara pair combination, and then para hydrogen pairs. The structural changes of graphene caused by chemisorbed hydrogen are discussed and are compared with existing experimental data and other theoretical calculations. The obtained results will be useful for nanoengineering of graphene by hydrogenation and for hydrogen storage.
Keywords: A1 Journal article; Condensed Matter Theory (CMT); Integrated Molecular Plant Physiology Research (IMPRES)
Impact Factor: 6.337
Times cited: 46
DOI: 10.1016/j.carbon.2011.03.052
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“Carbon clusters: from ring structures to nanographene”. Kosimov DP, Dzhurakhalov AA, Peeters FM, Physical review : B : condensed matter and materials physics 81, 195414 (2010). http://doi.org/10.1103/PhysRevB.81.195414
Abstract: The lowest-energy configurations of Cn(n≤55) clusters are obtained using the energy-minimization technique with the conjugate gradient method where a modified Brenner potential is invoked to describe the carbon and hydrocarbon interaction. We found that the ground-state configuration consists of a single ring for small number of C atoms and multiring structures are found with increasing n, which can be in planar, bowl-like or caplike form. Contrary to previous predictions, the binding energy Eb does not show even-odd oscillations and only small jumps are found in the Eb(n) curve as a consequence of specific types of edges or equivalently the number of secondary atoms. We found that hydrogenation of the edge atoms may change the ground-state configuration of the nanocluster. In both cases we determined the magic clusters. Special attention is paid to trigonal and hexagonal shaped carbon clusters and to clusters having a graphenelike configuration. Trigonal clusters are never the ground state while hexagonal-shaped clusters are only the ground state when they have zigzag edges.
Keywords: A1 Journal article; Condensed Matter Theory (CMT); Integrated Molecular Plant Physiology Research (IMPRES); Plasma Lab for Applications in Sustainability and Medicine – Antwerp (PLASMANT)
Impact Factor: 3.836
Times cited: 55
DOI: 10.1103/PhysRevB.81.195414
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“Reduction-enhanced water flux through layered graphene oxide (GO) membranes stabilized with H3O+ and OH- ions”. Gogoi A, Neyts EC, Peeters FM, Physical chemistry, chemical physics 26, 10265 (2024). http://doi.org/10.1039/D3CP04097F
Abstract: Graphene oxide (GO) is one of the most promising candidates for next generation of atomically thin membranes. Nevertheless, one of the major issues for real world application of GO membranes is their undesirable swelling in an aqueous environment. Recently, we demonstrated that generation of H3O+ and OH- ions (e.g., with an external electric field) in the interlayer gallery could impart aqueous stability to the layered GO membranes (A. Gogoi, ACS Appl. Mater. Interfaces, 2022, 14, 34946). This, however, compromises the water flux through the membrane. In this study, we report on reducing the GO nanosheets as a solution to this issue. With the reduction of the GO nanosheets, the water flux through the layered GO membrane initially increases and then decreases again beyond a certain degree of reduction. Here, two key factors are at play. Firstly, the instability of the H-bond network between water molecules and the GO nanosheets, which increases the water flux. Secondly, the pore size reduction in the interlayer gallery of the membranes, which decreases the water flux. We also observe a significant improvement in the salt rejection of the membranes, due to the dissociation of water molecules in the interlayer gallery. In particular, for the case of 10% water dissociation, the water flux through the membranes can be enhanced without altering its selectivity. This is an encouraging observation as it breaks the traditional tradeoff between water flux and salt rejection of a membrane.
Keywords: A1 Journal article; Condensed Matter Theory (CMT); Modelling and Simulation in Chemistry (MOSAIC)
Impact Factor: 3.3
DOI: 10.1039/D3CP04097F
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“Ground state configurations of two-dimensional plasma crystals under long-range attractive particle interaction force”. Chen Z, Kong M, Milošević, MV, Wu Y, Physica scripta 67, 439 (2003). http://doi.org/10.1238/Physica.Regular.067a00439
Keywords: A1 Journal article; Condensed Matter Theory (CMT); Plasma Lab for Applications in Sustainability and Medicine – Antwerp (PLASMANT)
Impact Factor: 1.28
Times cited: 4
DOI: 10.1238/Physica.Regular.067a00439
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“Modeling of chemical processes in the low pressure capacitive radio frequency discharges in a mixture of Ar/C2H2”. Ariskin DA, Schweigert IV, Alexandrov AL, Bogaerts A, Peeters FM, Journal of applied physics 105, 063305 (2009). http://doi.org/10.1063/1.3095760
Abstract: We study the properties of a capacitive 13.56 MHz discharge with a mixture of Ar/C<sub>2</sub>H<sub>2</sub> taking into account the plasmochemistry and growth of heavy hydrocarbons. A hybrid model was developed to combine the kinetic description for electron motion and the fluid approach for negative and positive ion transports and plasmochemical processes. A significant change in plasma parameters related to injection of 5.8% portion of acetylene in argon was observed and analyzed. We found that the electronegativity of the mixture is about 30%. The densities of negatively and positively charged heavy hydrocarbons are sufficiently large to be precursors for the formation of nanoparticles in the discharge volume.
Keywords: A1 Journal article; Condensed Matter Theory (CMT); Plasma Lab for Applications in Sustainability and Medicine – Antwerp (PLASMANT)
Impact Factor: 2.068
Times cited: 21
DOI: 10.1063/1.3095760
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“Theoretical study of the stable states of small carbon clusters Cn (n=210)”. Kosimov DP, Dzhurakhalov AA, Peeters FM, Physical review : B : solid state 78, 235433 (2008). http://doi.org/10.1103/PhysRevB.78.235433
Abstract: Both even- and odd-numbered neutral carbon clusters Cn (n=210) are systematically studied using the energy minimization method and the modified Brenner potential for the carbon-carbon interactions. Many stable configurations were found, and several new isomers are predicted. For the lowest energy stable configurations we obtained their binding energies and bond lengths. We found that for n5 the linear isomer is the most stable one while for n>5 the monocyclic isomer becomes the most stable. The latter was found to be regular for all studied clusters. The dependence of the binding energy for linear and cyclic clusters versus the cluster size n (n=210) is found to be in good agreement with several previous calculations, in particular with ab initio calculations as well as with experimental data for n=25.
Keywords: A1 Journal article; Condensed Matter Theory (CMT); Plasma Lab for Applications in Sustainability and Medicine – Antwerp (PLASMANT)
Impact Factor: 3.836
Times cited: 35
DOI: 10.1103/PhysRevB.78.235433
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“The formation of Cr2O3 nanoclusters over graphene sheet and carbon nanotubes”. Dabaghmanesh S, Neek-Amal M, Partoens B, Neyts EC, Chemical physics letters 687, 188 (2017). http://doi.org/10.1016/J.CPLETT.2017.09.005
Keywords: A1 Journal article; Condensed Matter Theory (CMT); Plasma Lab for Applications in Sustainability and Medicine – Antwerp (PLASMANT)
Impact Factor: 1.815
Times cited: 2
DOI: 10.1016/J.CPLETT.2017.09.005
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“Study of the intrinsic limitations of the contact resistance of metal/semiconductor interfaces through atomistic simulations”. Dabral A, Pourtois G, Sankaran K, Magnus W, Yu H, de de Meux AJ, Lu AKA, Clima S, Stokbro K, Schaekers M, Collaert N, Horiguchi N, Houssa M, ECS journal of solid state science and technology 7, N73 (2018). http://doi.org/10.1149/2.0041806JSS
Abstract: In this contribution, we report a fundamental study of the factors that set the contact resistivity between metals and highly doped n-type 2D and 3D semiconductors. We investigate the case of n-type doped Si contacted with amorphous TiSi combining first principles calculations with Non-Equilibrium Green functions transport simulations. The evolution of the intrinsic contact resistivity with the doping concentration is found to saturate at similar to 2 x 10(-10) Omega.cm(2) for the case of TiSi and imposes an intrinsic limit to the ultimate contact resistance achievable for n-doped Silamorphous-TiSi (aTiSi). The limit arises from the intrinsic properties of the semiconductors and of the metals such as their electron effective masses and Fermi energies. We illustrate that, in this regime, contacting heavy electron effective mass metals with semiconductor helps reducing the interface intrinsic contact resistivity. This observation seems to hold true regardless of the 3D character of the semiconductor, as illustrated for the case of three 2D semiconducting materials, namely MoS2, ZrS2 and HfS2. (C) The Author(s) 2018. Published by ECS.
Keywords: A1 Journal article; Condensed Matter Theory (CMT); Plasma Lab for Applications in Sustainability and Medicine – Antwerp (PLASMANT)
Impact Factor: 1.787
Times cited: 2
DOI: 10.1149/2.0041806JSS
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“Charge transfer doping modulated raman scattering and enhanced stability of black phosphorus quantum dots on a ZnO nanorod”. Hu L, Amini MN, Wu Y, Jin Z, Yuan J, Lin R, Wu J, Dai Y, He H, Lu Y, Lu J, Ye Z, Han S-T, Ye J, Partoens B, Zeng Y-J, Ruan S, Advanced Optical Materials 6, 1800440 (2018). http://doi.org/10.1002/ADOM.201800440
Abstract: Black phosphorus (BP) has recently triggered an unprecedented interest in the 2D community. However, many of its unique properties are not exploited and the well-known environmental vulnerability is not conquered. Herein, a type-I mixed-dimensional (0D-1D) van der Waals heterojunction is developed, where three-atomic-layer BP quantum dots (QDs) are assembled on a single ZnO nanorod (NR). By adjusting the indium (In) content in ZnO NRs, the degree and even the direction of surface charge transfer doping within the heterojunction can be tuned, which result in selective Raman scattering enhancements between ZnO and BP. The maximal enhancement factor is determined as 4340 for BP QDs with sub-ppm level. Furthermore, an unexpected long-term ambient stability (more than six months) of BP QDs is revealed, which is ascribed to the electron doping from ZnO:In NRs. The first demonstration of selective Raman enhancements between two inorganic semiconductors as well as the improved stability of BP shed light on this emerging 2D material.
Keywords: A1 Journal article; Condensed Matter Theory (CMT); Plasma Lab for Applications in Sustainability and Medicine – Antwerp (PLASMANT)
Impact Factor: 6.875
Times cited: 37
DOI: 10.1002/ADOM.201800440
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“Ionized water confined in graphene nanochannels”. de Aquino BRH, Ghorbanfekr-Kalashami H, Neek-Amal M, Peeters FM, Physical chemistry, chemical physics 21, 9285 (2019). http://doi.org/10.1039/C9CP00075E
Abstract: When confined between graphene layers, water behaves differently from the bulk and exhibits unusual properties such as fast water flow and ordering into a crystal. The hydrogen-bonded network is affected by the limited space and by the characteristics of the confining walls. The presence of an extraordinary number of hydronium and hydroxide ions in narrow channels has the following effects: (i) they affect water permeation through the channel, (ii) they may interact with functional groups on the graphene oxide surface and on the edges, and (iii) they change the thermochemistry of water, which are fundamentally important to understand, especially when confined water is subjected to an external electric field. Here we study the physical properties of water when confined between two graphene sheets and containing hydronium and hydroxide. We found that: (i) there is a disruption in the solvation structure of the ions, which is also affected by the layered structure of confined water, (ii) hydronium and hydroxide occupy specific regions inside the nanochannel, with a prevalence of hydronium (hydroxide) ions at the edges (interior), and (iii) ions recombine more slowly in confined systems than in bulk water, with the recombination process depending on the channel height and commensurability between the size of the molecules and the nanochannel height – a decay of 20% (40%) in the number of ions in 8 ps is observed for a channel height of h = 7 angstrom (bulk water). Our work reveals distinctive properties of water confined in a nanocapillary in the presence of additional hydronium and hydroxide ions.
Keywords: A1 Journal article; Condensed Matter Theory (CMT); Plasma Lab for Applications in Sustainability and Medicine – Antwerp (PLASMANT)
Impact Factor: 4.123
Times cited: 10
DOI: 10.1039/C9CP00075E
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“Out-of-plane permittivity of confined water”. Jalali H, Ghorbanfekr H, Hamid I, Neek-Amal M, Rashidi R, Peeters FM, Physical Review E 102, 022803 (2020). http://doi.org/10.1103/PHYSREVE.102.022803
Abstract: The dielectric properties of confined water is of fundamental interest and is still controversial. For water confined in channels with height smaller than h = 8 angstrom, we found a commensurability effect and an extraordinary decrease in the out-of-plane dielectric constant down to the limit of the dielectric constant of optical water. Spatial resolved polarization density data obtained from molecular dynamics simulations are found to be antisymmetric across the channel and are used as input in a mean-field model for the dielectric constant as a function of the height of the channel for h > 15 angstrom. Our results are in excellent agreement with a recent experiment [L. Fumagalli et al., Science 360, 1339 (2018)].
Keywords: A1 Journal article; Condensed Matter Theory (CMT); Plasma Lab for Applications in Sustainability and Medicine – Antwerp (PLASMANT)
Impact Factor: 2.366
Times cited: 38
DOI: 10.1103/PHYSREVE.102.022803
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“Cation-controlled permeation of charged polymers through nanocapillaries”. Faraji F, Neek-Amal M, Neyts EC, Peeters FM, Physical review E 107, 034501 (2023). http://doi.org/10.1103/PHYSREVE.107.034501
Abstract: Molecular dynamics simulations are used to study the effects of different cations on the permeation of charged polymers through flat capillaries with heights below 2 nm. Interestingly, we found that, despite being monovalent, Li+ , Na+ , and K+ cations have different effects on polymer permeation, which consequently affects their transmission speed throughout those capillaries. We attribute this phenomenon to the interplay of the cations' hydration free energies and the hydrodynamic drag in front of the polymer when it enters the capillary. Different alkali cations exhibit different surface versus bulk preferences in small clusters of water under the influence of an external electric field. This paper presents a tool to control the speed of charged polymers in confined spaces using cations.
Keywords: A1 Journal article; Condensed Matter Theory (CMT); Plasma Lab for Applications in Sustainability and Medicine – Antwerp (PLASMANT)
Impact Factor: 2.4
Times cited: 1
DOI: 10.1103/PHYSREVE.107.034501
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“Atomic level mechanisms of graphene healing by methane-based plasma radicals”. Khalilov U, Yusupov M, Eshonqulov Gb, Neyts Ec, Berdiyorov Gr, FlatChem 39, 100506 (2023). http://doi.org/10.1016/j.flatc.2023.100506
Keywords: A1 Journal article; Condensed Matter Theory (CMT); Plasma Lab for Applications in Sustainability and Medicine – Antwerp (PLASMANT)
Impact Factor: 6.2
DOI: 10.1016/j.flatc.2023.100506
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“Asymptotic expansions in the path integral approach to the bipolaron problem”. Smondyrev MA, Devreese JT, Peeters FM, Physical review : B : condensed matter and materials physics 51, 15008 (1995). http://doi.org/10.1103/PhysRevB.51.15008
Keywords: A1 Journal article; Condensed Matter Theory (CMT); Theory of quantum systems and complex systems
Impact Factor: 3.736
Times cited: 32
DOI: 10.1103/PhysRevB.51.15008
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