Overview of Drude-Lorentz type models and their applications

• Autorzy: Paolo Di Sia
• Języki publikacji: EN

Abstrakty

EN

This paper presents an overview of mathematical models for a better understanding of mechanical processes, as well as dynamics, at the nanoscale. After a short introduction related to semi-empirical and ab initio formulations, molecular dynamics simulations, atomic-scale finite element method, multiscale computational methods, the paper focuses on the Drude-Lorentz type models for the study of dynamics, considering the results of a recently appeared generalization of them for the nanoscale domain. The theoretical framework is illustrated and some examples are considered.

Słowa kluczowe

EN

Theoretical Modeling; Drude-Lorentz type Models; Computational Methods; Finite Element Methods; Nano-Bio-Technology

Kategorie tematyczne

• 83Axx: Special relativity
• 92Fxx: Other natural sciences (should also be assigned at least one other classification number in this section)
• 74Axx: Generalities, axiomatics, foundations of continuum mechanics of solids
• 82Dxx: Applications to specific types of physical systems
• 97Mxx: Mathematical modeling, applications of mathematics

• 03.30.+p: Special relativity
• 62.20.-x: Mechanical properties of solids
• 02.70.-c: Computational techniques; simulations(for quantum computation, see 03.67.Lx; for computational techniques extensively used in subdivisions of physics, see the appropriate section; for example, see 47.11.-j Computational methods in fluid dynamics)
• 73.63.-b: Electronic transport in nanoscale materials and structures(see also 73.23.-b Electronic transport in mesoscopic systems)
• 05.60.-k: Transport processes

• Wydawca: De Gruyter Open
• Czasopismo: Nanoscale Systems: Mathematical Modeling, Theory and Applications
• Rocznik: 2014
• Tom: 3
• Numer: 1

Daty

otrzymano

2012-07-09

zaakceptowano

2013-10-30

online

2014-03-20

Twórcy

autor

Paolo Di Sia

• Faculty of Education, Free University of Bolzano-Bozen, Viale Ratisbona 16, 39042
  Bressanone-Brixen, Italy

Bibliografia

• [1] K. T. Ramesh. Nanomaterials: Mechanics and Mechanisms. Springer, 353 pp., (2009).
• [2] T. J. R. Hughes. The Finite Element Method: Linear Static and Dynamic Finite Element Analysis. Dover Publications, 672 pp., (2000).
• [3] M. L. Bucalem and K-J. Bathe. The Mechanics of Solids and Structures - Hierarchical Modeling and the Finite Element Solution. Springer, 598 pp., (2011).
• [4] A. N. Cleland Foundations of Nanomechanics: From Solid-State Theory to Device Applications. Springer, 436 pp., (2003).
• [5] J.-L. Liu. Mathematical modeling of semiconductor quantum dots based on the nonparabolic effective-mass approximation. Nano MMTA, 1, 58, (2012).
• [6] J. L. Lopez and J. Montejo-Gamez. On the derivation and mathematical analysis of some quantum–mechanical models accounting for Fokker–Planck type dissipation: Phase space, Schrödinger and hydrodynamic descriptions. Nano MMTA, 2, 49, (2013).
• [7] J. R. Claeyssen, T. Tsukazan, L. Tonetto and D. Tolfo. Modeling the tip-sample interaction in atomic force microscopy with Timoshenko beam theory. Nano MMTA, 2, 124, (2013).
• [8] F. M. Borodich, B. A. Galanov, S. N. Gorb, M. Y. Prostov, Y. I. Prostov and M. M. Suarez-Alvarez. An inverse problem for adhesive contact and non-direct evaluation of material properties for nanomechanics applications. Nano MMTA, 1, 80, (2012).
• [9] F. X. Rlvarez, V. A. Cimmelli, D. Jou and A. Sellitto. Mesoscopic description of boundary effects in nanoscale heat transport. Nano MMTA, 1, 112, (2012).
• [10] A. Sellitto and F. X. Alvarez. Non-Fourier heat removal from hot nanosystems through graphene layer. Nano MMTA, 1, 38, (2012).
• [11] G. Panasenko. Multi-scale Modelling for Structures and Composites. Springer, 398 pp., (2005).
• [12] P. Gumbsch and R. Pippan. Multiscale Modelling of Plasticity and Fracture by Means of Dislocation Mechanics. Springer, 394 pp., (2010).
• [13] S. Attinger and P. D. Koumoutsakos. Multiscale Modelling And Simulation. Springer, 277 pp., (2004).
• [14] S. C. Singh, H. B. Zeng, C. Guo and W. Cai. Nanomaterials. John Wiley & Sons, 810 pp., (2012).
• [15] M. Ziman. Principles of the Theory of Solids. Cambridge University Press, 452 pp., (1979).
• [16] C. Kittel. Introduction to Solid State Physics. John Wiley & Sons, 766 pp., (2005).
• [17] Y. Gogotsi. Nanomaterials Handbook. CRC Press, 800 pp., (2006).
• [18] P. Di Sia. Classical and quantum transport processes in nano-bio-structures: a new theoretical model and applications. Faculty of Science, Verona University, Italy, PhD Thesis, 210 pp., (2011).
• [19] K. Binder and D. W. Heermann. Monte Carlo Simulation in Statistical Physics: An Introduction. Springer, 200 pp., (2010).
• [20] D. Vasileska and S. M. Goodnick. Nano-Electronic Devices: Semiclassical and Quantum Transport Modeling. Springer, 441 pp., (2011).
• [21] P. Di Sia. An Analytical Transport Model for Nanomaterials. J. Comput. Theor. Nanosci. 8, 84, (2011).
• [22] P. Di Sia. An Analytical Transport Model for Nanomaterials: The Quantum Version. J. Comput. Theor. Nanosci. 9, 31, (2012).
• [23] P. Di Sia. New theoretical results for high diffusive nanosensors based on ZnO oxides. Sens. & Transducers J. 122 (1), 1, (2010).
• [24] P. Di Sia. Oscillating velocity and enhanced diffusivity of nanosystems from a new quantum transport model. J. NanoR., 16, 49, (2011).
• [25] P. Di Sia. A new theoretical method for transport processes in nanosensoristics. J. NanoR., 20, 143, (2012).
• [26] P. Di Sia. Nanotechnology between Classical and Quantum Scale: Application of a new interesting analytical Model. Adv. Sci. Lett., 5, 1, (2012).
• [27] P. Di Sia. A new theoretical Model for the dynamical Analysis of Nano-Bio-Structures. Adv. Nano Res., 1 (1), 1, (2013).
• [28] P. Di Sia. About the Influence of Temperature in Single-Walled Carbon Nanotubes: Details from a new Drude-Lorentz-like Model. Appl. Surf. Sci., 275, 384, (2013).
• [29] P. Di Sia. Characteristics in Diffusion for High-Efficiency Photovoltaics Nanomaterials: an interesting Analysis. J. Green Sci. Technol., in press, (2013).
• [30] P. Di Sia. Relativistic motion in nanostructures: interesting details by a new Drude-Lorentz-like model. Conference Series, Third International Conference on Theoretical Physics Theoretical Physics and its Application, June 24-28, 2013, Moscow, Russia.
• [31] E. C. Fernandes da Silva. GaAs: effective-mass parameters. Data extract from Landolt-Börnstein III/44A: Semiconductors – New Data and Updates for I-VII, III-V, III-VI and IV-VI Compounds. Springer-Verlag, (2009).
• [32] I. Repins, M. Contreras, M. Romero, Y. Yan, W. Metzger, J. Li, S. Johnston, B. Egaas, C. DeHart, J. Scharf, B. E. McCandless and R. Noufi. Characterization of 19.9%-Efficient CIGS Absorbers. 33rd IEEE Photovoltaic Specialists Conference, May 11–16, San Diego, California, Preprint, (2008).
• [33] Available at: http://www.semiconductors.co.uk/propiivi5410.htm
• [34] J. M. Marulanda and A. Srivastava. Carrier Density and Effective Mass Calculation for carbon Nanotubes. Phys. Stat. Sol. (b), 245, 11, 2558, (2008).
• [35] H. Altan, F. Huang, J. F. Federici, A. Lan and H. Grebel. Optical and electronic characteristics of single walled carbon nanotubes and silicon nanoclusters by tetrahertz spectroscopy. J. Appl. Phys., 96, 6685, (2004). [Crossref]
• [36] I. Pirozhenko and A. Lambrecht. Influence of slab thickness on the Casimir force. Phys. Rev. A, 77, 013811, (2008). [Crossref]
• [37] C. A. Schmuttenmaer. Using Terahertz Spectroscopy to Study Nanomaterials. Terahertz Science and Technology, 1 (1), 1, (2008).
• [38] J. B. Baxter and C. A. Schmuttenmaer. Conductivity of ZnO Nanowires, Nanoparticles, and Thin Films Using Time- Resolved Terahertz Spectroscopy. J. Phys. Chem. B, 110, 25229, (2006). [Crossref]
• [39] P. Parkinson, H. J. Joyce, Q. Gao, H. H. Tan, X. Zhang, J. Zou, C. Jagadish, L. M. Herz and M. B. Johnston. Carrier Lifetime and Mobility Enhancement in Nearly Defect-Free Core−Shell Nanowires Measured Using Time-Resolved Terahertz Spectroscopy. Nano Letters, 9, 9, 3349, (2009). [Crossref]
• [40] P. Parkinson, J. Lloyd-Hughes, Q. Gao, H. H. Tan, C. Jagadish, M. B. Johnston and L. M. Herz. Transient Terahertz Conductivity of GaAs Nanowires. Nano Letters, 7, 7, 2162, (2007). [Crossref]
• [41] D. J. Aschaffenburg, M. R. C. Williams, D. Talbayev, D. F. Santavicca, D. E. Prober and C. A. Schmuttenmaer. Efficient measurement of broadband terahertz optical activity. Appl. Phys. Lett., 100, 241114 (5), (2012). [Crossref]
• [42] P. Di Sia. THz Spectroscopy and Nanostructures: a short interesting Review, Lett. Appl. NanoBioSci, 1 (!), 008, (2012).
• [43] P. Deák, T. Frauenheim and M. R. Pederson. Computer Simulation of Materials at Atomic Level. John Wiley & Sons, 727 pp., (2000).
• [44] S. Li and W. K. Liu. Meshfree Particle Methods. Springer, 502 pp., (2004).
• [45] J. Holman, A. Parsons, G. Pilling and G. Price. Chemistry: Introducing Inorganic, Organic and Physical Chemistry. Oxford University Press, 1440 pp., (2013).
• [46] D. Sholl and J. A. Steckel. Density Functional Theory: A Practical Introduction. John Wiley & Sons, 252 pp., (2011).
• [47] E. Engel and R. M. Dreizler. Density Functional Theory: An Advanced Course. Springer, 531 pp., (2011).
• [48] R. Car and M. Parrinello. Unified Approach for Molecular Dynamics and Density-Functional Theory. Phys. Rev. Lett., 55 (20), 2471, (1985). [Crossref]
• [49] T. Kühne, M. Krack, F. Mohamed and M. Parrinello. Efficient and Accurate Car-Parrinello-like Approach to Born- Oppenheimer Molecular Dynamics. Phys. Rev. Lett., 98 (6), 066401, (2007). [Crossref]
• [50] M. Avriel. Nonlinear Programming: Analysis and Methods. Courier Dover Publications, 512 pp., (2003).
• [51] J. Thijssen. Computational Physics. Cambridge University Press, 620 pp., (2007).
• [52] M. Yussouff and R. Zeller. An Efficient Korringa-Kohn-Rostoker Method for "complex" Lattices, Vol. 80, Vol. 166, Ed. International Centre for Theoretical Physics, (1980).
• [53] U. Mizutani. Introduction to the Electron Theory of Metals. Cambridge University Press, 590 pp., (2001).
• [54] J. A. C. Bland and H. Bretislav. Ultrathin Magnetic Structures I: An Introduction to the Electronic, Magnetic and Structural Properties. Springer, 350 pp., (2005).
• [55] K. Wandelt. Surface and Interface Science. John Wiley & Sons, Vols 1-2, 467 pp., (2012).
• [56] J. Wang. Key Issues of Classical Molecular Dynamics Simulation. Lambert Academic Publishing, 136 pp., (2010).
• [57] W. Tang. Molecular Dynamics Simulations of Carbon Nanotubes in Liquid Flow. ProQuest, 228 pp., (2007).
• [58] S. S. Vinogradov, P. D. Smith and E. D. Vinogradova. Canonical Problems in Scattering and Potential Theory Part II: Acoustic and Electromagnetic Diffraction by Canonical Structures. CRC Press, 520 pp., (2010).
• [59] M. Cherkaoui, L. Capolungo. Atomistic and Continuum Modeling of Nanocrystalline Materials: Deformation Mechanisms and Scale Transition. Springer, 387 pp., (2009).
• [60] C. Y. Fong, M. Shaughnessy, L. Damewood and L. H. Yang. Theory, Experiment and Computation of Half Metals for Spintronics: Recent Progress in Si-based Materials. NanoMMTA, 1, 1, (2012).
• [61] C. E. Burkhardt and J. J. Leventhal. Foundations of Quantum Physics. Springer, 530 pp., (2008).
• [62] P. J. Munson and R. K. Singh. Statistical significance of hierarchical multi-body potentials based on Delaunay tessellation and their application in sequence-structure alignment. Protein Science, 6, (7), 1467, (1997).
• [63] P. J. Munson, R. K. Singh. Statistical significance of hierarchical multi-body potentials based on Delaunay tessellation and their application in sequence-structure alignment. Protein Science, 6, 7, 1467, (1997).
• [64] W. K. Liu, E. G. Karpov, S. Zhang and H. S. Park. An introduction to computational nanomechanics and materials. Comput. Methods Appl. Mech. Engrg., 193, (17–20), 1529, (2004).
• [65] S. M. Musa. Computational Finite Element Methods in Nanotechnology. CRC Press, 640 pp., (2012).
• [66] J. Leszczynski. Trends in Computational Nanomechanics. Springer, 628 pp., (2010).
• [67] R. de Borst and E. Ramm. Multiscale Methods in Computational Mechanics: Progress and Accomplishments. Springer, 446 pp., (2011).
• [68] L. Mielke, T. Belytschko, and G. C. Schatz. Nanoscale Fracture Mechanics. Annu. Rev. Phys. Chem., 58, 185, (2007). [Crossref]
• [69] H. Gao, Y. Huang and F. F. Abraham. Continuum and atomistic studies of intersonic crack propagation. J. Mech. Phys. Solids, 49, 2113, (2001). [Crossref]
• [70] H. Van Swygenhoven, P. M. Derlet and A. Hasnaoui. Atomic mechanism for dislocation emission from nanosized grain boundaries. Phys. Rev. B, 66, 024101, (2002). [Crossref]
• [71] T. S. Gates, G. M. Odegard, S. J. V. Frankland and T. C. Clancy. Computational materials: Multi-scale modeling and simulation of nanostructured materials. Composites Science and Technology, 65, 2416, (2005).
• [72] P. Drude. Zur Elektronentheorie der metalle. Annalen der Physik, 306 (3), 566, (1900).
• [73] H. A. Bethe and A. Sommerfeld. Elektronentheorie der Metalle. Springer Verlag, 290 pp., (1967).
• [74] N. V. Smith. Classical generalization of the Drude formula for the optical conductivity. Phys. Rev. B, 64, 155106, (2001). [Crossref]
• [75] W. A. Goddard III, D. W. Brenner, S. E. Lyshevski and G. J. Iafrate. Handbook of Nanoscience, Engineering, and Technology. CRC Press, 1071 pp., (2012).
• [76] T. C. Choy. Effective Medium Theory: Principles and Applications. Oxford University Press, 182 pp., (1999).
• [77] M. G. Kuzyk. Polymer Fiber Optics: Materials, Physics, and Applications. CRC Press, 399 pp., (2010).
• [78] M. S. Green. Markoff Random Processes and the Statistical Mechanics of Time-Dependent Phenomena. II. Irreversible Processes in Fluids. J. Chem. Phys., 22, 398, (1954).
• [79] R. Kubo. Statistical-Mechanical Theory of Irreversible Processes. I. General Theory and Simple Applications to Magnetic and Conduction Problems. J. Phys. Soc. Jpn., 12, 570, (1957). [Crossref]
• [80] W. Rudin, Real and Complex Analysis, McGraw-Hill International Editions: Mathematics Series, McGraw-Hill Publishing Co, 416 pp., (1987).
• [81] P. J. Ventura, L. C. Costa, M. C. Carmo, H. E. Roman and L. Pavesi. AC Conductivity of Porous Silicon from Monte Carlo Simulations. J. Porous Materials, 7 (1-3), 107, (2000).
• [82] P. Di Sia. Present and Future of Nanotechnologies: Peculiarities, Phenomenology, Theoretical Modelling, Perspectives. Reviews in Theoretical Science (RITS), in press, (2014).
• [83] P. Di Sia. Effects on Diffusion by Relativistic Motion in Nanomaterial-Based Nanodevices. Conference Series, International conference “NANOSMAT-2013” (Granada-Spain) (September 22-25, 2013), in press (2013-2014).
• [84] D. Sridevi and K. V. Rajendran. Preparation of ZnO Nanoparticles and Nanorods by Using CTAB Assisted Hydrothermal Method. Int. J. Nanotech. Appl., 3 (2), 43, (2009).
• [85] J. B. Baxter and C. A. Schmuttenmaer. Carrier dynamics in bulk ZnO. II. Transient photoconductivity measured by timeresolved terahertz spectroscopy. Phys. Rev. B, 80 , 235206-1 10, (2009).[Crossref]

Identyfikatory

DOI

10.2478/nsmmt-2014-0001