Page - 63 - in Advanced Chemical Kinetics

3.2.Non-radiativeenergy transfer Inversely to the trivial mechanism, non-radiative energy transfer mechanisms are strictly dependent on the luminescence lifetime of the donor, since it only occurswhile the donor is in its electronic excited state. It needs the formationof a collision complexbetween thedonor andtheacceptorandtheenergy transferoccurswith the rightmoleculardistance: ð6Þ Its rate isgivenbythemagnitudeof the transitionmomentbetweentheelectronicwavefunction thatdescribes thecollisioncomplexbeforeandafter the transfer fromthedonor to theacceptor: ð7Þ Where is the complex wavefunction before the energy transfer and is thewavefunction thatdescribes thecomplexafter theenergy transfer. Dependingon thenatureof theenergy transfer, the intermoleculardistanceandthesimilarity of excited state energies, they can occur by a resonant mechanism called Forster resonance energy transfer (FRET)orbasedon theelectronexchangecalledDexterenergy transfer. 3.3.Forster resonantenergy transfer Energytransfer thatoccur inaratesimilar tothedonorfluorescence lifetimeinitially involvesa Coulombic interaction between the electronic excited state of the donor and the electronic groundstate of the acceptor that evolves to interactionof the acceptor electronic excited state with thedonorgroundstate.TheseCoulombic interactionsareonlypossibledueto theenergy proximity of the emission of thedonor and the absorption of the acceptor, enabling avirtual energytransfer, inwhichabsorptionandemissionof theenergyoccursimultaneously.Because the Coulombic interactions between the electronic states of both donor and acceptor occur during thedonor fluorescence lifetimeand theyarepredominant and represent the influence of thedipole-dipole interaction, theyaredependenton the inter-speciesdistancebya factorof r�3.Theprobabilityofoccurrenceof theenergy transfer, then, isproportional to the squareof thedistance,hence r�6.Therateof theenergy transfer isgivenby theForster expression [4]: ð8Þ Wherek2 istherelativeorientationofthedipoleofthedonorandtheacceptor,FDistheintensity of fluorescenceof thedonor,εAis theacceptorcoefficientofextinction,τDAis thedonor fluores- cence lifetimeinthepresenceof theacceptorandr is thedistancebetweendonorandacceptor. New Materials to Solve Energy Issues through Photochemical and Photophysical Processes: The Kinetics Involved http://dx.doi.org/10.5772/intechopen.70467 63