Exact solution to the general non-radiative energy transfer master equations in crystalline materials

Vega-Durán, J. T.; Dı́az-Torres, L.A.; Barbosa-Garcı́a, Oracio; Menéses-Nava, M. A.; Mosiño, J. F.

doi:10.1016/s0022-2313(00)00207-6

Cited by 14 publications

(17 citation statements)

References 16 publications

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“…The master equation is a phenomenological first‐order differential equation, which describes the time evolution of the probability for a system to be in a certain state out of a discrete set of states. It is often used in physics and chemistry, e.g., to describe diffusion processes (random walks), population dynamics, and chemical kinetics …”

Section: Simulation Of the Dynamicsmentioning

confidence: 99%

Comparison of different rate constant expressions for the prediction of charge and energy transport in oligoacenes

Stehr

Fink

Tafipolski

et al. 2016

WIREs Comput Mol Sci

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Charge and exciton transport in organic semiconductors is crucial for a variety of optoelectronic applications. The prediction of the material-dependent exciton diffusion length and the charge carrier mobility is a prerequisite for tailoring new materials for organic electronics. At room temperature often a hopping process can be assumed. In this work, three hopping models based on Fermi's Golden rule but with different levels of approximation-the spectral overlap approach, the Marcus theory, and the Levich-Jortner theory-are compared for the calculation of charge carrier mobilities and exciton diffusion lengths for oligoacenes, using the master equation approach and Monte Carlo simulations. Efor the donor deexcitation/neutralization and the analogue equation for the acceptor excitation/ionization respectively, the hopping rate, Eq. (1), can be written aswith the Franck-Condon weighted density of states (FCWD) 40,41,43WIREs Computational Molecular Science Prediction of charge and energy transport in oligoacenes using rate constant expressions Volume 6, November/December 2016Here, a linear approximation for e J E AD ð Þ is used, where J 0 : = d e J E AD ð Þ=dE AD j E AD = 0 and J : = e J 0 ð Þ, and thereforeEq. (14), the difference vector Δd ! of the equilibrium structures of the charged/excited state and the neutral/ground state is determined. This vector is transformed from Cartesian coordinates into a vector Δq ! in the normal mode basis viawhere the matrix A contains the normal mode vectors. The molecular vibrations are treated as harmonic oscillators. 50,55 Therefore, the relaxation Advanced Review

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Section: Simulation Of the Dynamicsmentioning

confidence: 99%

Comparison of different rate constant expressions for the prediction of charge and energy transport in oligoacenes

Stehr

Fink

Tafipolski

et al. 2016

WIREs Comput Mol Sci

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“…19 If these probabilities are again averaged over a large number of generated crystal samples, the resulting value converges to the probability of a macroscopic ensemble to remain excited at time t. Finally, the normalized macroscopic donor emissions D (t) is given by Similar expressions are obtained for the acceptor emission, A (t). 19 If these probabilities are again averaged over a large number of generated crystal samples, the resulting value converges to the probability of a macroscopic ensemble to remain excited at time t. Finally, the normalized macroscopic donor emissions D (t) is given by Similar expressions are obtained for the acceptor emission, A (t).…”

Section: Nonradiative Energy-transfer Processesmentioning

confidence: 94%

Energy Back-Transfer and other Nonradiative Energy-Transfer Processes in Yb[sup 3+], Er[sup 3+]:Y[sub 3]Al[sub 5]O[sub 12]

Barbosa-Garcı́a

Dı́az-Torres

Menéses-Nava

et al. 2002

J. Electrochem. Soc.

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Experimental data from two Yb 3ϩ , Er 3ϩ :yttrium aluminum garnet ͑YAG͒ crystal samples with different doping concentrations were analyzed through the calculation of the exact solution of the general nonradiative energy-transfer master equations. Besides the dipole-dipole direct energy transfer and the dipole-dipole migration processes assumed by other authors to predict the Yb 3ϩ -fluorescence decay, it is shown that a quadrupole-quadrupole direct energy transfer and a dipole-dipole back-transfer process are also present. The used free parameter values predicted our experimental data as well as other experimental data reported in the literature. Further, our modeling also calculates the acceptor transients which were also compared to experimental data. Therefore, the used modeling can be applied to analyze complicated nonradiative energy-transfer processes where traditional models fail.

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“…Y 2 O 3 is a cubic perovskite with spatial group symmetry Ia3 (206) [21,22]. Using the coordinate data from Crystallographic tables for the spatial group Ia3(206) [23] a kth nanocrystal sample is numerically generated. Then the Yb 3+ and Er 3+ dopant ions are placed into the potential 24d and 8b crystal sites with a random uniform distribution by using the Monte Carlo method.…”

Section: Model and Theorymentioning

confidence: 99%

Dynamics of the Green and Red Upconversion Emissions in Yb³⁺‐Er³⁺‐Codoped Y₂O₃ Nanorods

Meza

Dı́az-Torres

Salas

et al. 2010

Journal of Nanomaterials

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Efficient green and red upconversion emission inY2O3:Yb3+,Er3+nanorods under 978 nm radiation excitation is achieved. Experimental effective lifetimes, luminescent emissions, and nanorod sizes depend strongly on the solvent ratios used during the synthesis. A microscopic nonradiative energy transfer model is used to approach the dynamics of the green, red, and infrared emissions. The excellent agreement between simulated and experimental decay suggests that the energy transfer mechanisms responsible of the visible emission depend on the solvent ratio.

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Exact solution to the general non-radiative energy transfer master equations in crystalline materials

Cited by 14 publications

References 16 publications

Comparison of different rate constant expressions for the prediction of charge and energy transport in oligoacenes

Comparison of different rate constant expressions for the prediction of charge and energy transport in oligoacenes

Energy Back-Transfer and other Nonradiative Energy-Transfer Processes in Yb[sup 3+], Er[sup 3+]:Y[sub 3]Al[sub 5]O[sub 12]

Dynamics of the Green and Red Upconversion Emissions in Yb³⁺‐Er³⁺‐Codoped Y₂O₃ Nanorods

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Exact solution to the general non-radiative energy transfer master equations in crystalline materials

Cited by 14 publications

References 16 publications

Comparison of different rate constant expressions for the prediction of charge and energy transport in oligoacenes

Comparison of different rate constant expressions for the prediction of charge and energy transport in oligoacenes

Energy Back-Transfer and other Nonradiative Energy-Transfer Processes in Yb[sup 3+], Er[sup 3+]:Y[sub 3]Al[sub 5]O[sub 12]

Dynamics of the Green and Red Upconversion Emissions in Yb3+‐Er3+‐Codoped Y2O3 Nanorods

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Dynamics of the Green and Red Upconversion Emissions in Yb³⁺‐Er³⁺‐Codoped Y₂O₃ Nanorods