Excited state Exponential decay

If the intensity of the exciting light is modulated, the fluorescence light also shows a modulation at the same frequency cj, with a smaller degree of modulation and a phase shift against the modulation phase of the exciting light This phase shift is connected with the mean lifetime r of the excited state (exponential decay anticipated) by tg = CO T. 

We can see that for the second case, all we can observe is the nuclear excited-state exponential decay signal, no SRPAC signal can be observed. 

Various models are used in the literature to account for the kinetics of the excitons involved in optical processes. In the simplest cases, the signal evolution n(t) can be reproduced by considering either a single exponential or multiexponential time dependences. This model is well suited for solutions or solids in which monomolecular mechanisms happen alone. Since in most transient experiments the temporal response is a convolution of a Gaussian-shaped pulse and of the intrinsic kinetics, the rate of change with time of the excited-state population decaying exponentially is given by... 

In order to arrive at meaningful (exponential) decay rates in such experiments, non-linear triplet quenching by diffusion, has to be avoided. For example, the initial accelerated decay in Fig. 7 is caused by bimolecular triplet-triplet annihilation dominating the decay of the triplets. Similarly, a faster decay is observed at higher temperature, where triplet exciton diffusion to quenching sites is faster than monomolecular decay. Nevertheless, by using low temperatures and low excitation doses exponential decay kinetics are observed yielding radiative decay rates as low as 1 s x, which sets an upper limit for the triplet excited state lifetime [28,34],... 

The next process is the emission of a photon. As already mentioned, the emission of photons in a macroscopic system of fluorophores proceeds on the nanosecond timescale. This means that most photons are usually emitted and detected from excited states with fully relaxed solvate shell. Because the excited state population decays exponentially, fast measurements enable detection of hot photons from non-relaxed states at early times. When discussing the relaxation at the level of a single molecule, we have to consider different timescales. An isolated single emission event is as fast as the absorption, and the electronic transition takes less than 10 s. It is evident that the fluorophore does not reach the relaxed ground state immediately after the emission of a photon. What follows, is a cascade of processes that resemble the mirror image of the above-described relaxations. Firstly, the vibrational relaxation occurs and, finally, the solvent equilibrates corresponding to... 

For fluorescent compounds and for times in die range of a tenth of a nanosecond to a hundred microseconds, two very successftd teclmiques have been used. One is die phase-shift teclmique. In this method the fluorescence is excited by light whose intensity is modulated sinusoidally at a frequency / chosen so its period is not too different from die expected lifetime. The fluorescent light is then also modulated at the same frequency but with a time delay. If the fluorescence decays exponentially, its phase is shifted by an angle A([) which is related to the mean life, i, of the excited state. The relationship is... 

Nonradiative energy transfer is induced by an interaction between the state of the system, in which the sensitizer is in the excited state and the activator in the ground state, and the state in which the activator is in the excited and the sensitizer in the ground state. In the presence of radiative decay, nonradiative decay, and energy transfer the emission of radiation from a single sensitizer ion decays exponentially with time, /. 

The laser intensities are taken to be the possible lowest. The intensity in case (b) is almost three times larger than the others. This is simply due to the fact that the transition dipole moment exponentially decays from the equilibrium position and also the potential energy difference increases. Note again that the coordinate-dependent level approximation works well. In order to demonstrate the selectivity the time evolution of the wave packets on the excited state are shown in Fig 41. As a measure of the selectivity, we have calculated the target yield by... 

The value of k so determined could then be compared with the theoretical value of 4ttN aD. However, when viscosity is considerable and/or for short lifetimes, the transient effect in diffusion is not negligible and -30% of the transfer may be attributable to the transient phase. In such a case, the luminescence decay is not simply exponential (Sveshnikov, 1935). For a brief pulse excitation, a complicated decay ensures on the other hand, for so prolonged an excitation as to generate a steady state, the resultant decay curve in many cases is indistinguishable from an exponential (Yguerabide et ah, 1964). 

Flash photolysis studies with absorption or delayed fluorescence detection were performed to compare the binding of ground and excited state guests with DNA.113,136 The triplet lifetimes for 5 and 6 were shown to be lengthened in the presence of DNA.136 The decays were mono-exponential with the exception of the high excitation flux conditions where the triplet-triplet annihilation process, a bimo-lecular reaction, contributed to the decay. The residence time for the excited guest was estimated to be shorter than for the ground state, but no precise values for the rate constants were reported. However, the estimated equilibrium constants for the... 

If now we consider a large number of molecules N0, the fraction still in the excited state after time t would be N/N0 — e kt where N is the number unchanged at time t. This exponential law is familiar to chemists and biological scientists as the first-order rate law and by analogy fluorescence decay is a first-order process—plots of fluorescence intensity after an excitation event are exponential and each type of molecule has its own characteristic average lifetime. 

Fluorescence Lifetimes. The fluorescence decay times of TIN in a number of solvents (11.14.16.18.19), low-temperature glasses (12.) and in the crystalline form (15.) have been measured previously. Values of the fluorescence lifetime, Tf, of the initially excited form of TIN and TINS in the various solvents investigated in this work are listed in Table III. Values of the radiative and non-radiative rate constants, kf and knr respectively, are also given in this table. A single exponential decay was observed for the room-temperature fluorescence emission of each of the derivatives examined. This indicates that only one excited-state species is responsible for the fluorescence in these systems. 

In the case of a single exponential decay with time constant % (excited-state lifetime), the steady-state anisotropy is given by... 

The principles of pulse and phase-modulation fluorometries are illustrated in Figures 6.5 and 6.6. The d-pulse response I(t) of the fluorescent sample is, in the simplest case, a single exponential whose time constant is the excited-state lifetime, but more often it is a sum of discrete exponentials, or a more complicated function sometimes the system is characterized by a distribution of decay times. For any excitation function E(t), the response R(t) of the sample is the convolution product of this function by the d-pulse response ... 

Platinum and palladium porphyrins in silicon rubber resins are typical oxygen sensors and carriers, respectively. An analysis of the characteristics of these types of polymer films to sense oxygen is given in Ref. 34. For the sake of simplicity the luminescence decay of most phosphorescence sensors may be fitted to a double exponential function. The first component gives the excited state lifetime of the sensor phosphorescence while the second component, with a zero lifetime, yields the excitation backscatter seen by the detector. The excitation backscatter is usually about three orders of magnitude more intense in small optical fibers (100 than the sensor luminescence. The use of interference filters reduce the excitation substantially but does not eliminate it. The sine and cosine Fourier transforms of/(f) yield the following results ... 

Th fluorescence lifetime of a sample is the mean duration of time the fluorophore remains in the excited state. Following pulsed excitation, the intensity decays of many fluorophores are single exponential 2 23 ... 

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