Fluorescence Quenching by Electron TransferPurposeThe rate coefficient for quenching of the fluorescence of 9-cyanoanthracene byseveral electron-donor molecules will be measured. The rate coefficient for diffusion-limited encounter and the electron-transfer rate coefficient will be extracted from thequenching rate coefficient as a function of electron-transfer free energy.IntroductionFluorescence refers to photons emitted by molecules in excited states, as they return to their ground states. A fluorescence spectrophotometer measures the intensity of those photons. Quenching refers to reduction of fluorescence intensity by another molecule, one that causes some of the excited fluorescersto return to their ground states without emitting photons.A schematic diagram of a fluorescence spectrophotometer is atright. For a fluorescence spectrum, the exciting wavelengthλexc is held constant. Fluorescence intensity is measured whilethe emission wavelength, λem is scanned, producing thefluorescence spectrum. In this experiment, the fluorescingmolecule is 9-cyanoanthracene, "CNA." For an excitation spectrum, λexc is scanned while fluorescenceintensity is recorded at a single, fixed emission wavelength,λem. That produces an excitation spectrum (not shown atright).One way for a quencher, "Q," to reduce fluorescence fromCNA is for Q to transfer an electron to CNA. The rate coefficient for that transfer is referred to below as "ket." Before an electron can pass between Q and CNA, the two molecules must diffuse together. The rate coefficient for diffusing together is referred to as "kd," below.In this experiment, one measures quenching, then extracts kd and ket from the experimental results. As explained below, a kinetic mechanism leads to equations (mainly equations 4, 5, 20 and 21) that allow us to extract diffusion and electron-transfer rates from fluorescence data.TheoryA three-step mechanism suffices to illustrate quenching and the definition of the Stern-Volmer constant.Rate coefficients are shown to the right of each reaction.excitation A + υ→ A* kex(1)fluorescence A* → A+ υfkf(2)quenching A* +Q→ A + Q kq(3)Fluorescence intensity is proportional to the fluorescence rate, kf[A*]. Reaction 3 returns A* to the etQuench.odt 1Figure 2. spectrometer schematicFigure 1. CNAground state without emission of a photon, so Q is said to "quench" fluorescence. Assume the quencheris either present in excess, or absent, so [Q] is constant. The steady-state approximation for [A*] is [A*]Q = kex[A]/(kf + kq[Q]), When there is no quencher,[A*]0 = kex[A]/kf The ratio of unquenched ([Q]=0) to quenched intensity isI0/I = [A*]0/[A*]Q = 1 + (kq/kf)[Q]I0/I = 1 + kSV [Q] (4)The Stern-Volmer constant, kSV is defined to be the slope of I0/I versus [Q], so kSV = kq/kf. Because fluorescence lifetime τf = 1/kf, kSV also equals τf kq.kSV = τf kq(5)This experiment is based on the Journal of Chemical Education article by LarsPoulsen, et al.1 The quenching mechanism includes excitation and fluorescence,and also diffusive formation of an encounter complex and electron transfer within the encounter complex. A cyanoanthracene molecule, "A," is optically excited to an excited molecule, "A*". Excited cyanoanthracene either emits a photon, υf, or diffuses together with quencher molecule Q. Once in the encounter complex with Q, A* can be de-excited by electron transfer. Processes written as reactions, each with a rate coefficient, are below.excitation of cyanoanthracene: A + υex→ A* kex(6)fluorescence A* → A + υf kf(7)formation of the encounter complex: A* + Q → (A*···Q) kd(8)dissociation of the encounter complex: (A*···Q) → A* + Q k-d(9)electron transfer (A*···Q) → (A*-···Q+ ) ket(10)back electron transfer (A*-···Q+) → (A*···Q) k-et(11)other routes from A*- to its ground state (A*-···Q+) → A + Q kdecay(12)Although the electron-transfer quenching mechanism is more complicated than the first three-step mechanism, one can still identify a quenching constant kq as the steady-state effective-second-order ratecoefficient for nonradiative return of A to its ground state.nonradiative decay rate = kd[A*][Q] - k-d[A*···Q] (13)Assuming steady state, the time derivatives of concentrations of intermediates are set to zero.0 =d[A*⋯Q]dt = kd[A*][Q]-(ket+k-d) [A*···Q]+ k-et[A*-···Q+] 0 =d[A*-⋯Q+]dt= ket[A*···Q] - (kdecay + k-et) [A*-···Q+] etQuench.odt 2Figure 3. Stern-VolmerplotThe last equation, steady state for the ion pair, yields[A*-⋯Q+]=ket[A*⋯Q]kdecayk−etSubstituting that steady-state [A*-···Q+] into the steady-state equation for the collision-complex concentration, [A*···Q], and solving for [A*···Q] yields[A*⋯Q]=kd[ A*][Q ]ketk−d−k−etketkdecayk−etOne may substitute the above [A*···Q] into the non-radiative decay rate, equation 13. Then setting the nonradiative decay rate equal to kq[A*][Q] , one obtains after some algebra the following expression for the quenching rate constant kq.kq=kd11k−dketk−dkdecay1Ket(14)where Ket = ket/k-et is the equilibrium constant for electron transfer. Equation 14 can be found as equation 1 in the papers by Poulsen1 and Rehm and Weller2. The equilibrium constant can be written, ofcourse, in terms of the standard free energy of the electron-transfer reaction.Ket=e− Geto/ RT (15)The Gibbs free energy of electron transfer in the excited state isΔG°et = - ε°(Q) - ε°(CNA) - ΔE0,0 + ΔEsolvation(16)where ε°(Q) is the standard reduction potential of quencher Q, ε°(CNA) is the standard reduction potential of CNA, ΔE0,0 is the excitation energy of CNA, and ΔEsolvation is a correction for solvation energy of the ion pair. Values of ε° and ΔEsolvation are given in the calculations section, below.In this experiment, kdecay is large. That is, the excited anion A*- decays rapidly to its ground state. In that case, the third term in the denominator of equation 14 is negligible and the quenching constant is approximately the harmonic mean mean of diffusion and electron-transfer rate coefficients.1kq=1kd1Kdket(17)where Kd = kd/k-d is the equilibrium constant for forming the encounter complex, (A*···Q). Assuming that the encounter complex is only weakly bound, Kd≈1 M-1. That final approximation gives us the quenching rate coefficient kq as the harmonic mean of diffusion and electron-transfer rate coefficients.1kq=1kd1Mket(18)The "1M" numerator simply