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MODULE 19_03


The Deactivation of Excited Singlet States


As we have seen in earlier Modules the (stimulated) absorption (annihilation) of a photon by a molecule causes an electronic transition to occur with the concomitant formation of an excited electronic state. Quantum mechanical laws govern the photon-molecule interaction. In photophysics and photochemistry, 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 the ground states whence they originated and are therefore different chemical species, even though their nuclear framework may be identical or very similar to that of their ground state parent. Excited electronic states are intrinsically unstable and their excess energy can be dissipated in a variety of ways, physical and chemical. We can conveniently categorize the various decay routes into radiative and non-radiative (radiationless)



RADIATIVE DEACTIVATION PROCESSES BETWEEN STATES OF


LIKE MULTIPLICITY


UNLIKE MULTIPLICITY

Fluorescence Spin-allowed and strong



Phosphorescence

Spin-forbidden and weak





NON-RADIATIVE DEACTIVATION PROCESSES BETWEEN STATES OF:




LIKE MULTIPLICITY



UNLIKE MULTIPLICITY


Internal conversion

Very rapid



Intersystem crossing


Usually less rapid since spin-forbidden



Energy relationships and rate processes between electronic states are often depicted on a Jablonski diagram (Figure 19.1)







S1 radiative lifetimes are in the range 1 to 100 ns, although some are found outside this range. T1 radiative lifetimes are milliseconds and longer. Recall that the radiative lifetime is the reciprocal of the radiative rate constant. Thus



and



Since kFM is equal to the Einstein A coefficient, which is related to the Einstein B coefficient and then to the transition dipole moment , and then to the integrated extinction coefficient (J), it should come as no surprise that there is a relationship between kFM and J, thus



where nf and na are the mean refractive indices of the solvent over the fluorescence band and the absorption band, respectively, and



is the reciprocal of the mean value of -3 over the fluorescence spectrum. Equation (19.3) is the Strickler-Berg equation (1962). It allows a calculation of the radiative lifetime of fluorescence from a measurement of the absorption spectrum of the fluor.




The Jablonski method of presentation (Figure 19.1) is useful but it is confined to showing energy relationships only. Other factors are important when considering rates. An alternative approach is to think in terms of potential energy curves. For a diatomic molecule we can construct a potential energy curve such as shown in Figure 19.2. In such a molecule, quantized nuclear motions along the inter-nuclear axis provide a series of vibrational energy levels given by



For diatomics, every bound electronic state has a PE curve such as above. The curves are separated from each other on the energy axis. Different PE curves can intersect with each other depending on the curvature of the function (the force constant) and the value of r0.


FIGURE 19.3
It is not possible to characterize polyatomic molecules in the same precise 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 very useful physical picture can be gained for polyatomics, if we imagine that all the individual nuclear oscillators in the molecule are reduced to a single dimension, viz., a generalized nuclear coordinate. On this model we can represent a polyatomic in a Morse-type plot in an analogous way to what we do for diatomics where now the abscissa label become “general nuclear coordinate”. Another device we can employ is to regard the molecule in question as having a particular bond as the photochemically relevant entity, e.g. alkyl carbonyls. Then we can confine our attention to a “local mode” on that bond. This approximation is useful since it allows for energy level juxtapositions and curve crossings to be visualized. Figure 19.3 shows an example of this concept. Here we see the processes of absorption, internal conversion in S1, intersystem crossing and phosphorescence depicted. The vibrational cascade starts in S1 and continues until there is a curve crossing between S1 and T1. At that point, the isothermal intersystem crossing process can occur and there is some probability that the system will leave the crossing point on the triplet surface. Subsequent cascade takes the molecule to the v = 0 level of the triplet state whence phosphorescence can occur.

In effect, absorption and fluorescence are inverse processes. In solution phase at room temperature, most molecules are in lowest vibrational state (v = 0). Thus, upward transitions originate from v = 0 and terminate at = 0,1,2,3…in . The transition moments for the v = 0 to = n set of transitions vary (via the Franck-Condon factors) throughout the series, thus the efficiency of the individual absorption vibronic transitions varies through the series and the observed spectrum is a convolution of the set.

At the instant of absorption, the ensemble of molecules in electronic state will contain some in , some in , some in , and so on (Figure 19.3A). A radiative transition from can therefore originate from any of the set of vibrational states populated in the absorption process. However, all states above are capable of undergoing internal conversion (vibrational cascade) to . So a state is confronted by a choice of competing de-activation channels:

Fluorescence:

Internal conversion:

In most molecules the non-radiative process is much more rapid than the radiative one (; ). Therefore, as a general rule, the fluorescence transition originates from . This effect is called Kasha’s rule. One effect of this is to generate mirror symmetry between the absorption and fluorescence spectra of many chromophores. Figure 19.4 shows 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.


FLUORESCENCE MEASUREMENTS


Electronically excited states of molecule M can deactivate in several ways, some intramolecular and some bimolecular, as indicated in the accompanying scheme.


M + h M(S1)


N is the product of some intramolecular chemical change, e.g., cis-trans isomerization.

All the above processes (and more) may be competing in the de-activation of 1M*, and all are characterized by a rate constant. Only one of the processes is radiative (fluorescence) and by monitoring the fluorescence, either its intensity or lifetime, affords us a useful and convenient way of measuring the rate of decay of 1M*, and thence information on its reactivity.

There are two basic experimental set-ups:

(1) Steady state:


Continuous light source


Measures the fluorescence intensity as a function of wavelength.

(2) Time resolved:


Pulsed light source


Time-resolved detector


Measures fluorescence intensity as a function of time.

Steady State Spectrofluorimetry


Instrument schematic:




The source is a broadband lamp (usually Xe arc) operating in a continuous mode.

Monochromators are used to select narrow band of wavelengths from the excitation source and the emitted radiation.

Such instruments are often used to obtain excitation and emission spectra.

Excitation spectrum: fluorescence intensity at fixed and variable EX (comparison to absorption spectrum.)

Fluorescence Spectrum: fluorescence intensity at fixed and variable

A


FIGURE 19.8




typical observation may be seen in Figure 19.8.

T

Excitation

Fluorescence

he excitation spectrum provides information about the absorption spectrum of the molecules present that fluoresce. In a pure, uncomplicated 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 spectrum in this case will not closely resemble the absorption spectrum of the mixture.

Other factors also intervene to cause excitation and absorption spectra to differ.

Quantitative spectrofluorimetry:




Figure 19.9 shows a representation of a fluorescence spectrum. The area under the spectrum (GF) is proportional to the number of photons emitted. area (GF) under the fluorescence intensity vs. wavelength spectrum is proportional to the concentration of fluorescent states:



where qFM 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 . Under carefully controlled conditions, GF tracks the concentration of fluorescent states.

For example, consider the following experiment (Figure 19.10) in which a dilute solution of tetraphenylporphine (TPP) in benzene is examined with three different concentrations of oxygen in the solution, all under the same conditions of excitation. It is clear that the presence of oxygen causes an attenuation of the fluorescence signal. A plot of vs. has the form shown in Figure 19.11.


Oxygen is said to be a quencher of the fluorescence. The data obtained can be employed to extract quantitative information about the kinetic properties of the fluorescent species, as we see below.


A KINETIC SCHEME FOR FLUORESCENCE QUENCHING


Assume we have a solution of a fluorophore (such as the TPP above) in some solvent and there are no complications. Singlet states are populated in a continuous way by absorption of photons from the excitation light beam at the appropriate wavelength.


The states are depopulated via a variety of competing pathways:




Q represents a quencher of S1 such as oxygen, and Q’ represents the effects of the quenching act (non-specific). This quenching interaction is a bimolecular process. The excitation parameter, Rex, is a measure of the rate at which photons are absorbed into the sample. Since each photon absorbed generates one 1M* state, it also gives the rate of production (in molecules per second).

For a fixed ( you must be aware of the need for this) the amplitude of the fluorescence signal will depend on the competition between the fluorescence process (via) and all the other deactivation routes.

In the absence of quenchers, i.e., [Q] = 0






Under continuous, low-intensity irradiation, the concentration of rapidly builds up to a

low constant level and the steady-state approximation can be used, i.e.,



when




and since




then




The superscript '0' is used to indicate that [Q] = 0, and b is a proportionality (instrument) constant that takes into account light absorption, light gathering power, and detector sensitivity, etc.

When the quencher is present, i.e., [Q] > 0, another deactivation channel is added and





and proceeding as above and using the steady-state approximation:




and with b and REX arranged to be constant




where

It is usual to replace the product by KSV, the Stern-Volmer constant. Then,




The procedure is named the Stern-Volmer kinetic analysis, after the originators.


The Stern-Volmer Equation

The quantityis an observable, and is a linear function of the concentration of the quencher. Figure 19.12 represents a Stern-Volmer plot of the data in Figure 19.11.

Note that the intercept is unity as required by the S-V equation.


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 incorrect.

Since



this competition kinetics approach evaluates a ratio of rate constants (bimolecular/unimolecular).

Even though and can be very large, (approaching the theoretical limit), their relative magnitudes are available through the technique of competition kinetics. There is no requirement for time-resolved equipment to evaluate . The Stern-Volmer constant informs us how effectively the quencher can compete with the combination of the unimolecular deactivation pathways.

RELATIVE QUENCHING EFFICIENCIES

In a series of molecules, all of which will quench a given fluorescent state, their individual values express the different quenching efficiency.

Since , for quenchers we can write:



( 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 value, we can obtain the absolute values of the others.

What is ?

We defined as the sum of the rate constants that relate to intrinsic decay processes of . Further more we defined its inverse as being equal to a quantity we labeled M. The dimensions of are , thus those of  are s.

Suppose a collection of states is produced by a brief flash of light incident upon a solution of M. After the end of the flash, , thus, when [Q] = 0



(Here )

The above is a linear first-order differential equation, the solution of which can be written down, viz.,



or



After the flash, the population of excited states decays exponentially with time.

At time t = M,



Thus corresponds to that time at which the concentration of excited states has fallen to 1/e of the initial value.




is termed the FLUORESCENCE LIFETIME of the molecule M (absence of any bimolecular processes).

Even though we have defined through a consideration of excited state concentrations, it could equally well have been arrived at by considering fluorescence intensity time profiles, hence the name fluorescence lifetime. Note that, in general, the reciprocal of any unimolecular rate constant (s-1) has the dimensions of time and can be referred to as a lifetime. For example,



is termed the RADIATIVE LIFETIME.

We can employ fluorescence lifetime measurements in a similar way to the intensity measurements. Thus when [Q] = 0



and when [Q] > 0



then





is here defined as the measured lifetime when Q is present.

Values of M are usually in the range of 10-11 s to 10-7 s, with the largest representation being in the 1 to 10 ns range.


Examples covering the range are:

Rose Bengal in water 80 ps


Rose Bengal in 2 ns


Anthracene in cyclohexane 4 ns


Naphthalene in cyclohexane 95 ns


Pyrene in cyclohexane 450 ns

Some practicalities of quenching kinetics


From the above table it is apparent that fluorescence lifetimes are short and any technique that intends to measure such lifetimes must have a high time resolution. This is even more necessary when quenchers are present because then the lifetimes are even shorter. Moreover, any bimolecular reaxn that is to effectively quench fluorescence must possess a high bimolecular rate constant, since, from above



or



and



kM is the rate constant difference caused by the presence of Q. Effective quenching can be said to occur when , or more. If kM is 108 s-1 (10 ns lifetime), then kM = 4x108 s-1, or kQM[Q] = 4x108 s-1.

The product [Q] can be varied for a given Q by changing [Q] within the limits of solubility. Thus, when [Q]= M, the above [Q] product requires

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. Molecules that are free to diffuse in fluids will collide with each other at a rate which is governed by molecular size, solvent size, solvent viscosity, and temperature, if the species are uncharged; when charged, a Coulombic factor is involved (see a later Module). In solvents such as cyclohexane at RT, this diffusion-limited rate parameter has a value of ca (bimolecular, since collisional). This defines the upper limit of bimolecular rate constants for reactions that require collision. Many reactions have k values less than this because there are energy or entropic factors, which cause the efficiency on collision to be less than unity.

QUANTUM EFFICIENCIES AND QUANTUM YIELDS

The molecular quantum efficiency of fluorescence (qFM) is defined as the ratio of the number of photons emitted by an ensemble of molecular fluorophores to the number of molecules excited into the fluorescent (S1) state (which is equal to the number of photons absorbed).



Under conditions when some of the fluorescent states are quenched (by quencher Q) the fluorescence intensity is less than qFM and we use the term molecular fluorescence quantum yield (FM) to express this. In general

= Number of molecules of X converted per photon absorbed

=

=

e.g., 

= 



when quencher is absent.

The combination of quantum yield and lifetime measurements allows evaluation of the individual rate constants.


SIGNIFICANCE OF FLUORESCENCE STUDIES


Fluorescence arises from transition, i.e., is a property of an electronically excited state of a molecule. Thus we can learn about how the state deactivates and how it reacts with other molecules.

Fluorescence spectra give information on:

Vibrational spacing in ; efficiency of transitions (through FM).

Fluorescence lifetimes give information on:

  • Effectiveness of the radiative process.

  • Bimolecular rate constants and the reactivity of

(towards energy transfer, electron transfer, proton transfer, atom transfer, and other physical quenching processes)

SPECTROFLUORIMETRY: Practical considerations


As we saw above, under steady state excitation

With

With

Where


The most often used detector is a photomultiplier tube (PMT).


FIG.19.13

Each dynode stage contributes an amplification factor or 3-4 depending on applied voltage.

With 11 stages of gain (typical)



thus

You could check out these web sites for information about optics, instruments, etc.

(1) www.oriel.com

(2) www.acton-research.com


The PMT acts as a current source, which is run to ground via a load resistance (). A voltage-measuring device (CRO, digital device, etc) registers the voltage developed across .

Thus (Ohm’s Law), and VL is the measured quantity.

Now







m’ is an instrument constant

i.e.,

For a fluorescent sample under S-S illumination for [Q] = 0:








and



is the rate at which 1M* species are generated by the absorption of light



[The excitation source usually has a distribution]





[remember that ]

For non-monochromatic light sources and broadband absorbers, this needs summing over overlap region.

For small values of A() (< 0.1) we recognize that


And thus



or



where = and can be kept constant in a particular experiment.

Thus the quantum efficiency of fluorescence is directly proportional to the measured steady state voltage when the instrument conditions are carefully controlled.

Also, when a quencher is present:







Thus, the ratios for a series of [Q] measured in a spectrofluorimeter under constant irradiation and absorption conditions allow ratios of quantum yields to be determined and values to be extracted.


SOURCES OF ERROR IN SPECTROFLUORIMETRY


Self-absorption (inner filter effect)

The emitted photons must pass through the sample to reach the detector and will thus need to pass absorber molecules, when they have a chance of being reabsorbed. The probability of re-absorption will depend on the extent of the spectral overlap (see red segment of Figure 19.14). The higher the absorbance in the overlap region, the more the blue edge of the fluorescence will be distorted




.

The rule of thumb is to minimize absorbance in the overlap region by working at Aexc < 0.05 per cm.


Poor energy distribution-see schematic

Optics are designed for maximum excitation at and light collection from the center of cuvette.

If the absorbance at the excitation wavelength > 1, very little exciting radiation reaches center of sample and weak and distorted signals result.

In all fluorescence experiments keep the absorbance at the excitation wavelength as low as possible, consistent with sensitivity.




FLUORESCENCE LIFETIME INSTRUMENTATION124-126

Part of the following material has been excerpted and adapted from a review (hence the non-standard reference numbering) entitled “Photochemical Techniques” written by Kevin Henbest and myself for the series Electron Transfer in Chemistry, edited by Vincenzo Balzani and published by VCH in 2001


Introduction

Photon absorption by molecules can generate excited states that are fluorescent. The spin-allowed radiative process of fluorescence will be in competition with non-radiative deactivation modes and any bimolecular reactions and thus several processes will contribute to the overall decay of the excited state. The intrinsic lifetimes of fluorescent molecular states are typically in the range from 10-11 s to >10-8 s. The occurrence of bimolecular reactions involving the fluorescent state will shorten its lifetime , and thus measurement of changes of this quantity as a function of reactant concentration allows a computation of the r
ate constant for bimolecular reactions such as electron transfer. The kinetic scheme describing this situation has been discussed extensively above and in this addendum we focus on measurement techniques. In the past twenty years, time resolved measurements for fluorescence lifetime determination have become highly developed and they have been much used in electron transfer, energy transfer, proton transfer and other areas of research.

Sensitivity and specificity of fluorescence detection

Fluorescence detection is a very sensitive technique capable of measuring concentrations as low as one part in 1010. In comparison, absorption spectrophotometry is ca 103 times less sensitive. The superior sensitivity of fluorescence arises because fluorescence signals are measured relative to a zero background. The photomultiplier (or other detector) measures either photon arrival or no photon. In absorption spectrophotometry, the signal is determined from the difference between two light intensity measurements, one the test and one the reference. As the concentration of absorber is reduced, the test and reference signals will approach each other in magnitude and eventually the measurement of the small difference between two nearly equal large signals will become subject to large random error.

Instrumentation

Fluorescence Time Profiles




The ideal has an instantaneous rise because the excitation pulse is very short compared to the decay lifetime. The “not so clean” has excitation and decay proceeding in the same time window. We seek the ideal but sometimes have to compromise. The shorter the timescale, usually the worse things become.

Photoelectric DC Recording

In this method (see schematic) we use a light source that produces a short pulse to generate a fluorescence profile, then we pick up the emitted light in a collection system (lens), select a wavelength of interest and finally steer the fluorescence beam to a detector/signal processing unit.

The needs are for

  1. A generating impulse of zero width (a-function).

  2. A detection system of infinite temporal bandwidth and zero noise.

Generating impulse:

These days unbelievably short pulses are available from lasers (the current record is about 6 fs). So given the necessary financial resources, the generating function is not a problem. We discuss the technicalities later.

Detection system:

Three important factors:

  1. Detector sensitivity.

  2. Detector time response.

  3. Processor time response.

Sensitivity:

The detector has to convert photons to electrons thus the quantum efficiency of the photocathode (how many photons per photoelectron?) needs to be high and the noise background has to be low (Signal-to-Noise ratio). Photomultipliers are excellent in these respects and the Oriel website has lots of detail on response, noise and so forth.

Time response of PMT:

Approximate electron energy is 500 V, or a velocity of 4x106 ms-1

If distance traveled ~10 cm (cathode anode), time taken is 2x10-8 s = 20 ns.

Thus, the transit time for PMT is ca 20 ns.

This can be improved somewhat by good design, but few ns is typical.

Thus the input light pulse produces a replica electron pulse at anode, delayed by the transit time, of the PMT, tTr. Transit time per se is not the problem, since all it does is delay the appearance of the anode signal.


What really matters is the dispersion of transit times that arises from differences in the electron trajectories. Since the electron speeds are finite, different trajectories will result in different arrival times at the anode, even though they start at the same time. This represents degradation in information content.




This transit time dispersion is the limiting factor in determining the time resolution of the detector.
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