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 ψi ψj 1M0 ψi ψj hν For most organic molecules, the energies of the 1M0 → 1Mn transitions, ΔE, 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) as heat in a nonradiative process with rate constant knr, (2) by emitting a photon in a radiative process with rate constant kr, or (3) a separate molecule Q could interact with M and thus quench the excited state in a bimolecular process. (Discussed 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 solvent. However, within picoseconds (the actual time is solvent dependent), solvent 1 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, ΔE0,0, 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 this lab., you wil determine ΔE0,0 in this way for 9-cyanoanthracene (CNA). Figure 4. Absorption and emission spectra for a substituted indole. Question 2: Provide an explanation for the structure shown in both the absorption and emission spectra of Figure 3. In particular, comment on the spacing between the “bumps” 2 blue to avoid exciting the quenchers). Click on the camera icon, and save the spectrum: File/Save/Sample 3) Replace the teflon scatterer with your sample and switch the flash mode to multiple on the back of the white box. You might see already the fluorescence from CNA. 4) Maximize the signal/noise by playing with the strobe frequency, integration time, and average. Also, subtracting a Dark Spectrum will help a lot to reduce the noise: unclick Strobe/Lamp Enable, wait a few seconds, click on Store Dark (grey lamp icon), and then click on Subtract Dark Spectrum (grey lamp icon with a minus sign in front). Finally turn the Strobe/Lamp Enable back on. Keep in mind that every time you change either the integration time or the average a new Dark Spectrum should be acquired and subtracted. iv) Following the same procedure as in iii) measure the fluorescence of at least 5 different solutions of CNA (at the about the same concentration used for iii)) and each of the two quenchers. The concentration ranges that you should explore for the quenchers are: 1,4-dimethoxybenzene ~ (0.1 – 4.0) x 10-2 mol L-1 naphthalene ~ 0.1 – 0.8 mol L-1 Prepare these solutions in 25 ml volummetric flasks keeping good records of the dilutions you make since you will need to know the exact concentration of both quencher and fluorophor for the Stern-Volmer analysis. Make sure you use the same experimental conditions in iii) and iv) (integration time, average, frequency) v) Calculate I0 and I by either integrating the different emission spectra or just consider the intensity at a specific wavelength (which method has the largest error?). Keep in mind that I should be scaled by the dilution factor of CNA (for example, if the CNA solution from iii) was 2*10-5 M and one of the quenched solutions is 1.5*10-5 in CNA then I should be multiplied by 1.333) vi) Plot I0/I vs [Q] and run a linear regression to calculate kq for the two different quenchers, consider τ=11.6 +/- 0.1 ns. vii) If you need to store solutions to measure on the next lab period, do so in the S6 drawer. After you are done dispose of the solutions in the appropriate waste disposal bottle. 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 1M1 Q kdiff k-diff ket k-et kdecayM-. Q+. encounter pair + ...1M1 Q 1M0 Q+ radical ion pair 5 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 ψiψi ψjψj φiφi φjφj 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 experiment to confirm that the fluorescence quenching proceeds via electron 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 = 4πN (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. k-diff = 3 (DM + DQ) (rM + rQ)2 (18) 6 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, ΔGet, 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. With the simplistic molecular orbital diagram of Figure 5 in mind, it can be seen that one can estimate ΔGet 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, ΔE0,0 (equation 20). ΔGet ≅ E(Q/Q+.) - E(M-./M) - ΔE0,0 + 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, ΔG‡, 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 ΔG‡ will be Ket = ket k-et = e- ΔGet/RT (19) kij ≅ k ‡ e- ΔG ‡/RT (21) 7