1. MODULE 19(701) The Deactivation of Excited Singlet States The (stimulated) absorption (annihilation) of a photon by a ground state causes an electric dipole transition to occur to form an excited electronic state. Quantum mechanical laws govern the photon-molecule interaction. In the Photosciences we focus on the physical and chemical properties of the excited electronic state formed during the absorption process. Excited electronic states have different electronic configurations from their ground states and are therefore different chemical species, even though their nuclear framework may be identical or very similar to that of their ground state parent.

2. MODULE 19(701) Excited electronic states are intrinsically unstable. Their excess energy can be dissipated in a variety of ways, physical and chemical. The various decay routes can be categorized as “radiative” or “non-radiative” (radiationless). RADIATIVE TRANSITION BETWEEN STATES OF LIKE MULTIPLICITY RADIATIVE TRANSITION BETWEEN STATES OF UNLIKE MULTIPLICITY S 1  S 0 + h F Fluorescence Spin-allowed and strong T 1  S 0 + h P Phosphorescence Spin-forbidden and weak

3. MODULE 19(701) Energy relationships and rate processes connecting electronic states are often depicted on a Jablonski diagram RADIATIONLESS TRANSITIONS BETWEEN STATES OF LIKE MULTIPLICITY RADIATIONLESS TRANSITIONS BETWEEN STATES OF UNLIKE MULTIPLICITY S 2  S 1 + heat Internal conversion Very rapid S 1  T 1 + heat Intersystem crossing Spin forbidden and often slow

4. MODULE 19(701) T1T1 T2T2 T3T3 Intersystem crossing S2S2 S1S1 S0S0 absorptionfluorphosph internal conversion Intersystem crossing T3T3 T2T2 T1T1 Intersystem crossing

5. MODULE 19(701) S 1 radiative lifetimes are in the range 1 ns to 100 ns, (some notable exceptions). T 1 radiative lifetimes are milliseconds and longer. Recall that the radiative lifetime is the reciprocal of the radiative rate constant Since k FM is equal to the Einstein A coefficient, which is related to the Einstein B coefficient and then to  fi, and then to the integrated extinction coefficient (J), it should come as no surprise that there is a relationship between k FM and J.

6. MODULE 19(701) where n f and n a are the mean refractive indices of the solvent over the fluorescence and absorption bands, respectively The above is the Strickler-Berg equation. It allows a calculation of the radiative lifetime of fluorescence from a measurement of the absorption spectrum of the fluor.

7. MODULE 19(701) The Jablonski diagram is useful but it is confined to showing energy relationships between states. An alternative approach, useful for considerations of rates, is to use potential energy curves. For a diatomic molecule we can construct a potential energy curve as shown. Quantized nuclear motions along the inter-nuclear axis provide a set of vibrational energy levels.

8. MODULE 19(701) For diatomics, every bound electronic state has a PE curve as shown. The curves are separated from each other on the energy axis. Different PE curves can intersect each other depending on the curvature of the function (force constant) and the value of R eq. polyatomic molecules cannot be represented in the same manner as for diatomics since they have more than one degree of vibrational freedom. A multi-dimensional surface would be required for an equivalent characterization. However, an inaccurate, but useful picture can be gained for polyatomics, if we imagine that all individual nuclear oscillators in the molecule are reduced to a single dimension, viz., a generalized nuclear coordinate.

9. MODULE 19(701) On this model we represent a polyatomic in a Morse-type plot in an analogous way to what we do for diatomics where now the abscissa label becomes “general nuclear coordinate”. Also we can regard the molecule as having a particular bond as the relevant entity, e.g. alkyl carbonyls. Then we can confine our attention to a “local mode” on that bond. This approach allows for energy level juxtapositions and curve crossings to be visualized  see Figure.

10. MODULE 19(701) Absorption and fluorescence are inverse processes. In solution phase at room temperature, most molecules are in lowest vibrational state (v = 0), and upward transitions originate in v = 0 and terminate at v’ = 0,1,2,3…in S 1. The transition moment dipoles for the v = 0 to v’ = n set of transitions vary (via the Franck-Condon factors) throughout the series. Thus the efficiency of an individual absorption vibronic transition varies along the series and the observed spectrum is a convolution of the set.

11. MODULE 19(701) At the instant of absorption, the ensemble of molecules in S 1 will contain some in several of the vibrational states (Fig.). A radiative transition from S 1 can therefore originate from any of the set of vibrational states populated in the absorption process. However, all states above v’ = 0 are capable of undergoing internal conversion (vibrational cascade) to v’ = 0.

12. MODULE 19(701) So a molecule formed in a higher vibrational level of S 1 is confronted by a choice of undergoing fluorescence or internal conversion (vibrational cascade). In most molecules the non-radiative process is much more rapid than the radiative one (k nr ~ 10 11 s -1 ;k rad ~ 10 8 s -1 ). As a general rule, fluorescence originates from S 1 (v’ = 0). This effect is called Kasha’s rule.

13. MODULE 19(701) One effect of this is to generate mirror symmetry between the absorption and fluorescence spectra of many chromophores. Figure gives an example of this for a silicon phthalocyanine in toluene solution. This symmetry is only found for molecules that undergo minimal nuclear geometry change on excitation.

14. MODULE 19(701) FLUORESCENCE Electronically excited states of molecule M can deactivate in several ways, both unimolecular and bimolecular, as indicated. M + h A  M(S 1 ) M + h F M(T 1 ) +  M(S 0 ) +  N +  Bimolecular processes N is formed from M(S 1 ) in some unimolecular chemical change, e.g., cis-trans isomerization.

15. MODULE 19(701) All the above processes (and more) may be competing in the de- activation of M(S 1 ), and all are characterized by a rate constant. Only one of the processes is radiative (fluorescence). Monitoring the fluorescence, either its intensity or lifetime, affords a useful and convenient way of measuring the rate of decay of 1M*, and thence information about its reactivity. There are two types of instruments: Steady-state (cw): measures the fluorescence intensity as a function of wavelength. Time-resolved: measures the fluorescence intensity as a function of time.

16. MODULE 19(701) Steady-state instruments (spectrofluorimeters) are used to obtain excitation and emission spectra. Excitation spectrum: fluorescence intensity at fixed EM and variable  X (comparison to absorption spectrum.) Fluorescence Spectrum: fluorescence intensity at fixed  X and variable EM

17. MODULE 19(701) An excitation spectrum provides information about the absorption spectrum of the molecules present that fluoresce. For a one-component fluor solution, sample, the excitation spectrum closely resembles the absorption spectrum. In a mixture where only one component is fluorescent, the excitation spectrum will be that of the fluorescent compound only, but the absorption spectrum will contain additional bands. The excitation and absorption spectra will be dissimilar. excitation

18. MODULE 19(701) Quantitative spectrofluorimetry The area under the I F vs. spectrum, (G F ), is proportional to the number of photons emitted and thence to the concentration of emitting states. q FM is the molecular quantum efficiency of fluorescence. In many cases and in such cases a measurement of the peak intensity can be used to follow changes in G F Under carefully controlled conditions, G F tracks the concentration of fluorescent states.

19. MODULE 19(701) For example, consider an experiment in which a dilute solution of tetraphenylporphine (TPP) in benzene is examined at three oxygen concentrations under the same conditions of excitation. Oxygen causes attenuation of the fluorescence signal. IFIF / nm 0 mM 2 mM 10 mM A plot of I max vs. [O 2 ] has the form shown in the next Figure. Oxygen is said to be a quencher of the fluorescence.

20. MODULE 19(701) These data can be employed to extract quantitative information about the kinetic properties of the fluorescent species. IFIF [O 2 ] N 2 saturated Air-saturated O 2 saturated

21. MODULE 19(701) A KINETIC SCHEME FOR FLUORESCENCE QUENCHING Assume we have a solution of a fluor(ophore) (such as TPP) in some solvent and there are no complications. Singlet states are populated in a continuous way by absorption of photons from cw excitation light at the appropriate wavelength. 1 M* states are depopulated via a variety of competing pathways:

22. MODULE 19(701) Q represents a quencher of S 1 (such as oxygen). Q’ represents the effects of the quenching act (non-specific). Note that quenching is a bimolecular process. The excitation parameter, R ex, is a measure of the rate at which photons are absorbed into the sample. Since each photon absorbed generates one 1 M* state, it also gives the rate of production of excited states (in mol s -1 ). For a fixed R ex (important) the amplitude of the fluorescence signal will depend on the competition between the fluorescence process (via k FM ) and all the other deactivation routes.

23. MODULE 19(701) In the absence of quenchers ([Q] = 0) Under cw, low-intensity irradiation [ 1 M*] rapidly builds up to a low constant level and the steady-state approximation can be used, i.e.,

24. MODULE 19(701) Since The superscript '0' indicates that [Q] = 0. b is a proportionality (instrument) constant When [Q] > 0, another deactivation channel is added

25. MODULE 19(701) Defining  M as and This analysis is named the Stern-Volmer kinetic analysis, after its originators, and K SV is the Stern-Volmer constant. G F 0 /G F is measurable, and is a linear function of [Q]. Note that the intercept is unity as required by the S-V equation. G 0 /G [O 2 ] 1.0

26. MODULE 19(701) Whenever you make a S-V plot and it is not linear or does not have an intercept of unity you must suspect that the kinetic scheme you are using is not correct. Recall that this competition kinetics approach evaluates a ratio of rate constants (bimolecular/unimolecular). Even though k QM and Σk i can be very large (approaching the theoretical limit), their relative magnitudes are available through the competition kinetics method. There is no requirement for time-resolved equipment. The Stern-Volmer constant informs us how effectively the quencher can compete with the total unimolecular deactivation.

27. MODULE 19(701) Relative quenching efficiency In a series of quenchers, their individual k QM values express the different quenching efficiencies. For the quenchers Q 1, Q 2, Q 3, … we can write: (since  M is an intrinsic property of the fluorescent state and is independent of the quencher) Thus we can evaluate the SV coefficient ratios. And if we can obtain an absolute value for one k QM value, we can obtain the absolute values of the others.

28. MODULE 19(701)  M We defined Σ i k i as the sum of the rate constants that relate to intrinsic decay processes of 1 M*. Furthermore we defined its inverse as being equal to a quantity we labeled  M. The dimensions of Σ i k i are s- 1, thus those of  M are s. Suppose an ensemble of 1M* states is produced by a brief flash of light incident upon a solution of M. A the end of the flash R ex = 0, thus when [Q] = 0

29. MODULE 19(701) After the flash, the population of excited states decays exponentially with time. At time t =  M Thus  M corresponds to that time at which the concentration of excited states has fallen to 1/e of the initial value.  M is the FLUORESCENCE LIFETIME of M (no bimolecular processes). We have defined   via excited state concentrations. We could equally well have used fluorescence intensity time profiles, hence the name fluorescence lifetime.

30. MODULE 19(701) In general, the reciprocal of any unimolecular rate constant (s -1 ) has the dimensions of time and can be called a lifetime. For example, we saw above the RADIATIVE LIFETIME We can derive the SV equation in terms of lifetimes, Thus when [Q] = 0 And when [Q] > 0

31. MODULE 19(701)  M values fall in the range 10 -11 s to 10 -7 s, with most in the 1 to 10 ns range. COMPOUNDLIFETIME/NS ROSE BENGAL/WATER0.08 ROSE BENGAL/ACN2.0 ANTHRACENE/c-HEX4.0 NAPHTHALENE/c-HEX95 PYRENE/c-HEX450

32. MODULE 19(701) Some practicalities of quenching kinetics Fluorescence lifetimes are short and so any technique that intends to measure them must have a high time resolution. When quenchers are present then the lifetimes are even shorter. A bimolecular reaxn that is to effectively quench the fluorescence process must possess a high bimolecular rate constant, e.g.

33. MODULE 19(701)  k M is the rate constant difference caused by the presence of Q. Effective quenching occurs when k M ’/k M = 5, or more. If k M is 10 8 s -1 (10 ns lifetime), then  k M ~ 4x10 8 s -1, or k QM [Q] = 4x10 8 s -1. The product k QM [Q] can be varied by changing [Q] within the limits of solubility. Thus, when [Q]= 10 -2 M, the above [Q] product requires k QM = 4x10 10 It turns out that such a value for a bimolecular rate constant between normal-sized molecules in a mobile solvent represents the "diffusion-limited" value. (more later)

34. MODULE 19(701) QUANTUM EFFICIENCIES AND QUANTUM YIELDS The molecular quantum efficiency of fluorescence (q FM ) is the ratio of the number of photons emitted by a population of fluorophores to the number of molecules excited into the fluorescent (S 1 ) state (i.e. the number of photons absorbed). Under conditions when some of the fluorescent states are quenched (by Q) the fluorescence yield is less than q FM and we use the term molecular fluorescence quantum yield (  FM ) to express this.

35. MODULE 19(701)  X = Number of molecules of X converted per photon absorbed = No quencher The combination of quantum yield and lifetime measurements allows evaluation of the individual rate constants.

36. MODULE 19(701) SIGNIFICANCE OF FLUORESCENCE STUDIES Fluorescence results from an electric dipole transition. It is a property of an electronically excited state of a molecule. It informs about how the state deactivates and how it reacts with other molecules. Fluorescence spectra give information on: Vibrational spacing in S 0 Efficiency of v’ = 0 to v = 0, 1, 2, …transitions (via  FM ).

37. MODULE 19(701) Fluorescence lifetimes give information on: Effectiveness of the radiative process. Bimolecular rate constants and the reactivity of S 1 (towards energy transfer, electron transfer, proton transfer, atom transfer, and other physical quenching processes). In the section “SPECTROFLUORIMETRY: practical considerations” you will find a development of how the light collected is converted into a voltage signal and how this can be employed to generate the SV relationship. Following that is a section on errors.

38. MODULE 19(701) The Module ends with an adaptation from a recent review written by Kevin Henbest and myself. There is a lot of detail about fluorescence lifetime measurements. Basically there are four kinds of experiments that can be used for a determination of  1photoelectric DC recording 2Time-correlated single photon counting 3Fluorescence up-conversion 4Phase shift determination To a large extent the one you choose depends on the lifetime of the excited state you are interested in.