Abstract
In this paper, we propose an original functional method that makes it easy to determine the effect of any deviation in the shape of a nano-object from the well-studied shape (e.g., spherical) on the quantum characteristics of charge localized inside the nano-object. The maximum dimension of the object is determined by the magnitude of influence of quantum-size effects on quantum states of charge, and is limited by 100 nm. This method is ideologically similar to the perturbation theory, but the perturbation of the surface shape, rather than the potential, is used. Unlike the well-known variational methods of theoretical physics, this method is based on the assumption that the physical quantity is a functional of surface shape. Using the method developed, we present the quantum-size state of charges for two different complex shapes of nano-objects. The results from analyzing the quantum-size states of charge in the nano-objects with a deformed spherical shape indicated that the shape perturbations have a larger effect on the probability density of locating a particle inside the nano-object than on the surface energy spectrum and quantum density of the states.
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References
Auvinen S, Alatalo M, Haario H, Jalava JP, Lamminmaki RJ (2011) Size and shape dependence of the electronic and spectral properties in TiO2 nanoparticles. J Phys Chem C 115:8484–8493
Dvoyan KG, Kazaryan EM, Petrosyan LS (2005) Electronic states in quantum dots with ellipsoidal symmetry. Phys E 28:333–338
Dzyuba VP (2006) Scalar-vector methods of theoretic acoustics. Dalnauka, Vladivostok
Forestiere C, Miano G, Boriskina S, Negro L (2009) The role of nanoparticle shape and deterministic aperiodicity for the design of nanoplasmonic arrays. Opt Express 17(12):9648–9660
Kulchin YuN, Dzyuba VP, Shcherbakov AV (2009) Optical transmittance spectra of insulator nanoparticles in bulk heterocomposites. Semiconductors 43(3):331–339
Kulchin YuN, Dzyuba VP, Voznesenskiy SS (2011) Threshold optical nonlinearity of dielectric nanocomposite. In: Reddy B (ed) Advances in diverse industrial applications of nanocomposites. InTech, Rijeka, pp 261–288
Kwang-Hyon Kim, Hisakou A, Herrman J (2010) Linear and nonlinear optical characteristics of composites containing metal nanoparticles with different sizes and shapes. Opt Express 18(7):7488–7496
Landau LD, Lifshitz EB (2002) Quantum mechanics. Fizmatlit, Moscow
Li J, Wang L-W (2003) Shape effects on electronic states of nanocrystals. Nano Lett 3(10):1357–1363
Li L, Hu J, Yang W, Paul AA (2011) Band gap variation of size- and shape-controlled colloidal CdSe quantum rods. Nano Lett 1(7):349–351
Lin Z, Franceschetti A, Lusk MT (2011) Size dependence of the multiple exciton generation rate in CdSe quantum dots. ACS Nano 5(4):2503–2511
Matthew CB, Turner MG, Schmuttenmaer CA (2002) Size-dependent photoconductivity in CdSe nanoparticles as measured by time-resolved terahertz spectroscopy. Nano Lett 2(9):983–987
Migdal AB (1975) Qualitative methods in quantum theory. Science
Moreels I, Lambert K, Smeets D, De Muynck D, Nollet T, Martins JC, Vanhaecke F, Vantomme A, Delerue C, Allan G, Hens Z (2009) Size-dependent optical properties of colloidal PbS quantum dots. ACS Nano 3(10):3023–3030
Mors PM, Feshbach H (1953) Methods of theoretical physics. McGraw-Hill, New York
Shmelev AB (1972) Wave scattering by statistically uneven surfaces. Physics Uspekhi 15:173–183
Stetz AW (2006) Advanced quantum mechanics
Stroyuk OL, Dzhagan VM, Shvalagin VV, Kuchmiy SYa (2010) Size-dependent optical properties of colloidal ZnO nanoparticles Charged by photoexcitation. J Phys Chem C 114:220–225
Sucu S, Mese AI, Okan SE (2008) The role of confinement and shape on the binding energy of an electron in a quantum dot. Phys E 40:2698–2702
Xu H, Chen X, Ouyang S, Kako T, Ye J (2012) Size-dependent Mie’s scattering effect on TiO2 spheres for the superior photoactivity of H2 evolution. J Phys Chem C 116:3833–3839
Acknowledgments
This work was supported by Grant Nos. 12-I-0-02-010 and 12-I-0-02-055 of Presidium of Russian Academy of Science.
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Dzyuba, V., Kulchin, Y. & Milichko, V. Effect of the shape of a nano-object on quantum-size states. J Nanopart Res 14, 1208 (2012). https://doi.org/10.1007/s11051-012-1208-7
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DOI: https://doi.org/10.1007/s11051-012-1208-7