Determination of an Excited-State Electron-Transfer Rate Constant by Fluorescence Quenching | CHEM 114, Lab Reports of Physical Chemistry

Download Determination of an Excited-State Electron-Transfer Rate Constant by Fluorescence Quenching | CHEM 114 and more Lab Reports Physical Chemistry in PDF only on Docsity! Experiment S6 Chemistry 114 Determination of an Excited-State Electron-Transfer Rate Constant by Fluorescence Quenching. (i) Absorption and Emission of Light: A given molecule M in the ground state, denoted 1M0, can interact with electromagnetic radiation, absorb a photon, and thus populate an excited electronic state of M. The Franck-Condon allowed, vertical transition populates an excited state denoted 1Mn, where the subscript n indicates the excited electronic level. A schematic representation of such a transition is shown in Figure 1, with different vibrational sublevels, v and v’, of a given state. Figure 1. A state energy diagram that illustrates key aspects of light absorption and emission. The rate constants knr and kr are defined in the text. Using the HOMO-LUMO convention, this process can be illustrated as shown in Figure 2. 1M1 i j 1M0 i j h For most organic molecules, the energies of the 1M0  1Mn transitions, E, are such that the absorbed light generally falls in the UV or visible regions of the electromagnetic spectrum. The 1Mn state initially formed upon light absorption almost always relaxes very quickly to populate the v’=0 level of the lowest excited singlet state, 1M1 (Figure 1). This is called the Kasha rule. Depopulation of the 1M1(v’=0) state can proceed by several competing pathways: (1) the energy of 1M1 excitation may be lost as heat in a nonradiative process with the rate constant knr, (2) the 1M1 state can lose its excitation energy by emitting a photon in a radiative process with the rate constant kr, or (3) a separate molecule Q could interact with M and thus quench the excited state in a bimolecular process. (Discussed further below). In the process of light absorption by a solute M dissolved in a solvent, the transition originates from a state in which the solvent is in equilibrium with the charge distribution of the solute. Using the 1M0  1M1 transition as an illustration (Figure 3), the 1M1 state created upon light absorption can have a significantly different charge distribution than the 1M0 state. Because the solvent does not immediately respond to this change in solute charge distribution, the 1M1 state initially produced is not in equilibrium with the surrounding 1 solvent. However, within picoseconds (the actual time is solvent dependent), solvent reorientation yields a lower energy, equilibrated 1M1 state. Upon light emission the change in solute charge density, associated with the 1M1  1M0 transition, is likewise not in equilibrium with the surrounding solvent, and an equilibrated state is again achieved only after solvent reorientation. This sequence of events is illustrated in Figure 3. Figure 3. Potential energy curves that illustrate events associated with light absorption and emission in a generic solute/solvent system. Question 1: In drawing potential energy curves such as those shown in Figure 3, axes are often omitted. What is the x-axis usually implied in such drawings. Furthermore, the 1M1 potential energy curve is shifted to the right with respect to the 1M0 potential energy curve. What is the justification for this? As can be inferred from the diagrams in Figures 1 and 3, the spectral profile of fluorescence is generally shifted to longer wavelength than the spectral profile of absorption. The difference between the peak maxima of these two spectra is called the Stokes shift. A reasonable estimate of the energy gap between the 1M1(v’=0) level and the 1M0(v=0) level, E0,0, can be obtained by determining the point at which the fluorescence and absorption profiles cross each other when scaled to the same peak amplitude (see example in Figure 4). In the course of these laboratory exercises, it will be necessary to determine E0,0 in this way for 9-cyanoanthracene (CNA). Figure 4. Absorption and emission spectra for a substituted indole. 2 Suggested concentration ranges for each quencher (for a concentration of CNA such that the max. absorption is around 0.1): 1,4-dimethoxybenzene ~ (0.07 – 1.0) x 10-2 mol L-1 naphthalene ~ 0.1 – 0.8 mol L-1 Quenching via Electron Transfer: One possible mechanism by which a quencher Q can deactivate an excited electronic state is via a process of electron transfer. Key steps in such a process are illustrated below: Scheme 1: Briefly, 1M1 and Q must first diffuse together to form an encounter pair in which the distance between 1M1 and Q, the so-called interaction distance, is appropriate for the transfer of an electron. The rate of this diffusion-dependent encounter is related to the magnitude of the bimolecular rate constant kdiff. Of course, once formed, the encounter pair can diffuse apart to regenerate 1M1 and Q. The rate of this process is related to the unimolecular rate constant k-diff. Once the encounter pair has formed, electron transfer can occur with the rate constant ket to generate the radical ion pair. A simplistic molecular orbital diagram illustrating this process is shown in Figure 5. (In scheme 1, we show electron transfer from Q to 1M1. However, depending on the redox potentials of both M and Q, it is also reasonable to consider electron transfer from 1M1 to Q.) M-. Q+. 1M1 Q ket ii jj ii jj electron transfer Figure 5. Simplistic molecular orbital diagram that illustrates the process of electron transfer in the 1M1-Q encounter pair to produce a radical ion pair. If one were to monitor the quenching of 1M1 fluorescence by some molecule Q, and if the mechanism of quenching proceeded via the events shown in Scheme 1, then the overall quenching rate constant, kq, could be expressed as a function of the individual rate constants shown in Scheme 1. For the system as shown, this expression is given in equation 16, where the equilibrium constant for electron transfer, Ket, is equal to the ratio ket/k-et of the respective rate constants for electron transfer. kq = kdiff 1 + k-diff ket + k-diff kdecay 1 Ket (16) You will use equation 16 to calculate values of kq for the two quenchers used for the Stern-Volmer experimental to confirm that the fluorescence quenching proceeds via electron 5 1M1 Q kdiff k-diff ket k-et kdecay M-. Q+. encounter pair + ...1M1 Q 1M0 Q+ radical ion pair transfer. The necessary theory and experimental values for the different rate constants is presented below: (i) Diffusion-controlled rate constants, kdiff and k-diff. In the Smoluchowski equations, the rate constants for diffusion-limited processes are expressed as a function of the solvent-dependent diffusion coefficients, D, of the respective reaction partners (equations 17 and 18). Thus, in this case, the coefficients of concern are DM and DQ, both expressed using the standard units of cm 2/s. The other parameter that must be considered is the distance at which M and Q are said to interact. This interaction distance is sometimes expressed as the sum of the interaction radii for M and Q, rM and rQ, respectively. The bimolecular rate constant kdiff for diffusion-limited encounter of two solvated species M and Q is shown in equation 17 where N is Avogadro’s number. (Note: In the present context, kdiff should be expressed with the units of mol -1 L s-1). kdiff = 4N (rM + rQ) (DM + DQ) (17) By the same token, the unimolecular rate constant for diffusion dependent dissociation of the encounter pair can be expressed by equation 18. In this study, the molecules M and Q are approximately the same size and thus have approximately the same diffusion coefficient in the solvent acetonitrile: DM ~ DQ ~ 2-3 x 10 -5 cm2/s. A reasonable estimate for the M-Q interaction distance is 6 Å. (ii) Equilibrium constant for electron transfer, Ket. As shown in equation 19, the equilibrium constant for electron transfer, Ket, can be expressed as a function of the Gibbs energy difference, Get, between the encounter pair and the radical ion pair. This Gibbs energy for electron transfer can be illustrated as the difference between the minima of potential curves for the encounter pair and the radical ion pair (Figure 7). Figure 7. Potential curves that illustrate an exothermic electron transfer process. The x-axis represents changes that occur upon electron transfer in (1) the solvation shell surrounding the M-Q pair, and (2) the configuration of nuclei in the M-Q pair. 6 k-diff = 3 (DM + DQ) (rM + rQ)2 (18) Ket = ket k-et = e- Get/RT (19) With the simplistic molecular orbital diagram of Figure 5 in mind, it can be seen that one can estimate Get for electron transfer from Q to M using the oxidation potential of Q, E(Q/Q+.), and the reduction potential of M, E(M-./M). Specifically, one must consider the energy that must be put into the system to remove an electron from Q, and the energy that will be gained when M acquires an electron. However, since M in this system is in an excited state, 1M1, one must account for the energy of M excitation, E0,0 (equation 20). Get  E(Q/Q+.) - E(M-./M) - E0,0 + Esolv (20) When writing equation 20, it is important to recognize that we have included a term, Esolv, to account for the energy associated with the Coulombic attraction of the positive and negative charge in the radical ion pair. In the polar solvent acetonitrile, the medium in which our experiments will be done, this energy is ~ -5 kJ/mol. (iii) Rate constant for ion pair decay to generate ground states, kdecay. In general, the rate constant for a given process from i to j, kij, can be expressed as a function of the activation barrier, G‡, for this process (equation 21). We now apply equation 21 to obtain an estimate for kdecay. With respect to Scheme 1, we assume that the process of electron transfer is sufficiently exothermic so that G‡ will be very small. Under these conditions, the overall rate constant kij will thus be defined by the frequency factor k‡. For a process in acetonitrile, this will be on the order of 1-4 x 1011 s-1. (iv) Rate constant for electron transfer from Q to 1M1, ket. As shown in equation 21, the rate constant for this process of electron transfer, ket, can be expressed as a function of the activation barrier for electron transfer, Get ‡. It thus becomes necessary to find an approach by which Get ‡ can be estimated. As illustrated in Figure 7, Get ‡ can be represented by considering the point at which the 1M1-Q and M -.-Q.+ potential surfaces intersect. Upon further examination of Figure 7, it should become apparent that the magnitude of this activation energy will depend on the energy difference between the minima of the respective potential surfaces (i.e., Get ‡ will depend on Get). In a landmark study on electron-transfer reactions, R. Marcus used parabolas to represent the 1M1-Q and M -.-Q.+ potential surfaces and, from this, was able to write an expression showing the dependence of Get ‡ on Get (as an aside, Marcus was awarded the Nobel prize in chemistry for this seminal work on electron transfer reactions). Over the years, a variety of different expressions have evolved showing how Get ‡ can depend on Get. One such expression, derived by Rehm and Weller, accounts for the diffusion-controlled limit of reactions in solution and is given in equation 22. Get ‡ = Get 2 2 + Get ‡ (0) 2 1/2 + Get 2 (22) By using this expression, Rehm and Weller were able to model the experimental observation that, for sufficiently negative values of Get, the reaction proceeds at the diffusion-controlled limit (i.e., kij = kdiff). In equation 22, Get ‡(0) represents the activation energy for electron transfer in a thermoneutral reaction where Get = 0, and for our present study we will assume that Get ‡(0) = 10 kJ/mol. 7 kij  k ‡ e- G ‡/RT (21)