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Grand Canonical Monte Carlo Method for Predicting Hydrogen Adsorption Tyllianakis Emmanuel 1* , Klontzas Emmanuel 2 , Dimitrakakis K. Georgios 2 , Mpourmpakis Giannis 2 and Frudakis George E. 2 1 Material Science and Technology Department, University of Crete, P.O. Box 2208, Heraklion, Crete, 71003, Greece 2 Department of Chemistry, University of Crete, P.O. Box 2208, Heraklion, Crete, 71003, Greece *tilman@materials.uoc.gr A lot effort has been devoted for the study of interaction between hydrogen and nanostructures, in an effort for the hydrogen uptake to be calculated. From theoretical point of view, the only way to study this hydrogen adsorption is the Grand Canonical Monte Carlo method, since it permits the total number of particles adsorbed to fluctuate, whereas the chemical potential, μ, the cell volume, V, and the temperature, T, are kept constant i.e. (μ, V, T) ensemble. In this way, the pressure and temperature experimental conditions can be simulated, since the chemical potential is explicitly calculated for the specific thermodynamic state. Three types of motions occur during the simulation i.e. particle displacement, creation, and destruction. These different steps are executed with equal frequency. In a creation step, the position of the new particle is chosen randomly within pore volume V and its potential energy U is calculated. Finally these steps are accepted with the probability min(1; P) with ⎛ U − μ ⎞ V ⎛U − μ N P = exp ⎜− ⎟ P creation destruction ⎝ kBT ⎠ N + 1 k BT ⎟ ⎞ ⎛ U1 −U 2 ⎞ = exp ⎜ P = ⎝ ⎠ V ⎜− ⎟ displacement exp ⎝ k BT ⎠ Prior to the GCMC simulation, the exact value of chemical potential for the specific thermodynamic condition is needed, as referred earlier. For that purpose the Widom test particle method [1] is implemented for bulk hydrogen, at densities that correspond to that condition. The basic idea of this method is to try to insert at regular intervals, a particle at a random position. The particle is assumed to have no difference on the rest of the system, but it has an energy, the average of which is used for the calculation of chemical potential. The correct form of the function that describes the non-bonded interactions is the central point of this method and to that direction a lot of classical effective potentials have been used. Among them the Lennard-Jones is the one, most widely used. According to this potential, the interaction between a pair of particles i and j separated by a distance r is given by the equation 12 6 ⎡⎛ σ ⎤ ij ⎞ ⎛σ ij ⎞ V ⎢⎜ ⎟ − ⎜ ⎟ ⎥ ij = 4 ⋅ε ij ⎢ ⎥ ⎣⎝ rij ⎠ ⎝ rij ⎠ ⎦ where i and j denote hydrogen or carbon particles. ε describes the potential depth and σ is the size potential parameters. Besides this potential, some other functions have also been used like the Silvera-Goldman [2], the Crowell-Brown [3] etc. The main disadvantage of these potentials is the use of uniform parameters for a given pair of heteroatoms and hence the absence of varying these values according to the particularities of the system under examination. For that purpose, Monte Carlo method has often to corporate with accurate ab initio methods for the exact value of these parameters to be calculated. In addition to these potential some other terms are used also to describe other kind of interactions like electrostatic interactions, or the contributions of quantum effects which have been proven to contribute significally [4] especially at lower temperatures. The application of GCMC methods allows us to compare the efficiency of different nano-structures to adsorb hydrogen and study the contributions of some factors to that uptake. In that sense, a variety of simulations on different systems has been performed, including from graphene sheets and carbon nanotubes, that were the first systems to attract the scientific interest concerning hydrogen uptake, to more novel materials proposed like carbon nanoscrolls and metal organic frameworks. Some representative results from these calculations can be seen at Figures 1-5. Figure 1: GCMC calculations for (9-9) nanotube arrays with 0.7 nm intertube distance at pressure of 10 MPa and temperatures of 77, 175 and 293 K. 193
Figure 3: GCMC calculations for undoped and Li ion doped nanoscroll at 10 MPa and 293 K. Figure 4: Top view and side view of snapshots from GCMC calculation on new proposed material for hydrogen adsorption. Figure 5: Snapshots from GCMC calculation on Li – doped metal organic framework, IRMOF-14. [1] B. Widom. Some topics in the theory of fluids. J. Chem. Phys., 39, 2802, (1963). [2] I.F. Silvera and V.V. Goldman, J. Chem. Phys., 69, 1, (1978). [3] A. D. Crowell and J. S. Brown, Surf. Sci. 123, 296 (1982). [4] P. Kowalczyk, R. Hołyst, A. P. Terzyk and P. A. Gauden, Langmuir, 22, 1970 (2006). [5] P. Kowalczyk, H. Tanaka, R. Hołyst, K. Kaneko, T. Ohmori and J. Miyamoto, J. Phys. Chem, 109 17174 (2005). 194
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XXIII ΠΑΝΕΛΛΗΝΙΟ ΣΥΝΕ
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Κοιτώντας τα πρακτ
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ΕΠΙΤΡΟΠΕΣ Οργανωτι
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ΠΡΟΓΡΑΜΜΑ ΣΥΝΕΔΡΙΟ
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21. Οργανικά τρανζίσ
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15:30 15:45 16:00 16:15 16:30 16:45
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41. Modeling and quantitative phase
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Ανοιχτή Συνεδρία «
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«NανοΥλικά και Νανο
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New materials and MOS device concep
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Reliability Characteristics of Rare
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Ο λόγος των ταχυτήτ
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Thus the mean R In-In is expected t
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FIG 1. Schematic representation of
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με 0.80 eV στη διεπιφά
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Εντοπισµός Φορέων
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Παρασκευή και Xαρακ
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Electrical Spin Injection from Fe i
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Electrical Spin Injection of Spin-P
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References [1] CH Lee, J. Meteer, V
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Σχήμα 1: Φωτογραφία
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SEM Image Layout Simulation Εικ
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Μελέτη Ατελειών Σε
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Facet-Stress-Driven Ordering in SiG
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νανοκρυσταλλίτης (a
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Σχήµα 1. Εικόνες περ
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Σχήµα 1. Εικόνες περ
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Οι δομές που αναπτύ
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Raman Intensity (10 -50 cm 3 ) 1,2
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Μελέτη της Επίδρασ
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Annealing Induced Dissociation of N
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`Εναπόθεση με Παλμι
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Μελέτη της Χημείας
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Ανάπτυξη Νέων Μεσο
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Application of Thermal Quadrupoles
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Στοχαστική προσομο
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Νανοτραχύτητα κατά
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Ευαισθησία και Δια
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Optical Properties of CuIn 1-x Ga x
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ανοπτημένο με λέιζ
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Στο σχήμα 3 φαίνοντ
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Id (mA) -0,3 -0,2 -0,1 Vg=0 Vg=-1 V
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Strained-Si Si 1-x Ge x graded Si 1
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Fig. 1. Laser mask movement during
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forwarded to the back interface dur
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Σχήμα 2: Εκθετική εξ
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V th (V) G m,max /G m,max0 (%) I d
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C/ C ox 1,0 0,8 0,6 0,4 0,2 0,0 -4
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και Ta 2 O 5 , των οποίω
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κατασκευή της. Η πα
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ΔP (mW) 12 10 8 6 4 2 0 0 500 1000
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υπολογίσουμε θεωρη
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Σχήμα 2 Σύστημα ηλε
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Μελέτη των Μηχανισ
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Ανάπτυξη και Μελέτ
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Structure and Magnetic Properties o
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Δομή και Μαγνητικέ
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Μετρήσεις Ειδικής
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Further, almost all of the observed
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g-factor 2.019 2.016 2.013 2.010 2.
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ρυθμό 4 C.min -1 , έπειτ
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ΜΕΛΕΤΗ ΤΟΥ ΦΑΙΝΟΜΕ
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Νέοι Εξαφερίτες Ba µ
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Crystal Structure of a new Supramol
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Magnetic Phase Transition in Synthe
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Συσχέτιση πλαστική
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Μετασχηματισμοί φά
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Μελέτη της Επίδρασ
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Resonant Spin Transfer Torque in Do
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3 η Προφορική Συνεδ
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technology, and e-beam lithography.
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ecause it reduces the calculation o
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Υπολογισμός Υψηλής
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The thermodynamic average is obtain
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ΑΠΟΤΕΛΕΣΜΑΤΑ Στην
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προερχόµενη είτε α
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Combining Magnetism and Ferroelectr
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υµένια LCMO/STO (100) πολ
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Our scheme is illustrated in Fig. 1
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[6] . Η μελέτη του υλι
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τα πειραµατικά µας
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συµπύκνωµα. Αυτό επ
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Page 215: [1] S. Iijima, Nature 354, 56 (1991
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6 η Προφορική Συνεδ
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Ηλεκτρομαγνητική Α
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Φασματοσκοπική Μελ
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Thermal and Electrical Properties o
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Structure, Mechanical, and Optoelec
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Designing Nanoporous Materials for
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This program was developed to serve
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Νέα Αυτό-οργανούμε
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A Physical Model to Interpret the E
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FIR study of Ag x (As 33 S 33 Se 33
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Mελέτη Μεικτών Γυαλ
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The Structural Role of Fe and Zn in
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ΕΥΡΕΤΗΡΙΟ ΣΥΓΓΡΑΦΕ
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Κομπίτσας Μ…………
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ΕΥΡΕΤΗΡΙΟ ΣΥΓΓΡΑΦΕ
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W Watson I.M………………4 Weg
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