By Pedro Ludwig Hernández Martínez, Alexander Govorov, Hilmi Volkan Demir
This short provides a whole research of the generalized thought of Förster-type strength move in nanostructures with combined dimensionality. the following the purpose is to procure a generalized thought of be anxious together with a accomplished set of analytical equations for all mixtures and configurations of nanostructures and deriving conventional expressions for the dimensionality concerned. during this short, the amendment of agonize mechanism with appreciate to the nanostructure serving because the donor vs. the acceptor could be integrated, targeting the rate’s distance dependency and the position of the potent dielectric functionality in be troubled, for you to be a distinct, invaluable resource if you happen to learn and version FRET.
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Additional resources for Understanding and Modeling Förster-type Resonance Energy Transfer (FRET): FRET from Single Donor to Single Acceptor and Assemblies of Acceptors, Vol. 2
Rev. B 76, 125308/1– 125308/16 (2007) 5. L. O. V. Demir, Generalized theory of Förster-Type nonradiative energy transfer in nanostructures with mixed dimensionality. J. Phys. Chem. C 117, 10203–10212 (2013) 38 3 Nonradiative Energy Transfer in Assembly of Nanostructures 6. G. Kim, S. Okahara, M. G. Shim, Experimental veriﬁcation of Förster energy transfer between semiconductor quantum dots. Phys. Rev. B 78, 153301/1–153301/4 (2008) 7. M. L. A. J. K. Gun’ko, V. Lensyak, N. , Concentration dependence of Förster resonant energy transfer between donor and acceptor nanocrystals quantum dots: Effects of donor-donor interactions.
3 Schematic for the energy transfer of a NP → 3D NP assembly, b NW → 3D NP assembly, and c QW → 3D NP assembly. Orange arrows denote the energy transfer direction. Yellow circles represent an exciton in the α-direction. d is the separation distance. h0 is the azimuthal angle between d and r. [Reprinted (adapted) with permission from Ref. 10) boils down to 2 Z1 Z1 Z1 2 edexc 2 3 3e0 b ca ¼ a RNPA Im jeNPA ðxÞj h eeffD eNPA ðxÞ þ 2e0 0 À1 À1 qNP x2 þ y2 þ ðz þ d Þ2 3 dxdydz ð3:15Þ The ﬁnal equation for the transfer rate is obtained as 2 2 edexc 2 pR3NPA qNP 3e0 Im jeNP ðxÞj ca ¼ ba A 3 h eeffD 6 d eNPA ðxÞ þ 2e0 ð3:16Þ For this case, the distance dependency for the energy transfer rate is proportional to d À3 , similar to the bulk case .
In the following section the results obtained in Chap. 2 (Ref. ) are used to derive expressions for the assembly cases. 1 Energy Transfer Rates for Nanoparticle, Nanowire, or Quantum Well to 1D Nanoparticle Assembly The FRET rate analytical equations are derived in the long distance approximation, when the donor is an NP, an NW, or a QW while the acceptor is a 1D NP assembly (linear chain) (Fig. 1). 1; e0 is the medium dielectric constant; RNPA and eNPA are the acceptor NP radius and dielectric function, respectively; and r is the distance between the donor and linear NP chain (Fig.
Understanding and Modeling Förster-type Resonance Energy Transfer (FRET): FRET from Single Donor to Single Acceptor and Assemblies of Acceptors, Vol. 2 by Pedro Ludwig Hernández Martínez, Alexander Govorov, Hilmi Volkan Demir