Nonradiative decay rate

The occurrence of nonradiative losses is classically illustrated in Figure 3. At sufficiently high temperature the emitting state relaxes to the ground state by the crossover at B of the two curves. In fact, for many broad-band emitting phosphors the temperature dependence of the nonradiative decay rate P is given bv equation 1 ... 

Substitution of the exponential term from (6) into (7) replaces the free-volume term by the solvent viscosity and provides an equation for the viscosity-dependent nonradiative decay rate, from which the quantum yield emerges (8) ... 

The lifetime, therefore, depends not only on the intrinsic properties of the fluorophore but also the characteristics of the environment. For example, any agent that removes energy from the excited state (i.e., dynamic quenching by oxygen) shortens the lifetime of the fluorophore. This general process of increasing the nonradiative decay rates is referred to as quenching. 

Herein, F is the radiative decay rate and km is the nonradiative decay rate, which comes from quenching. It has been demonstrated that silica nanomatrixes can change the fluorescence quantum yield and lifetime of fluorophores. Several groups have reported that both quantum yield and lifetime of fluorophores increased in DDSNs [27, 28, 52, 65-67]. However, the mechanisms regarding this enhancement were reported differently. 

In contrast, the nonradiative decay rate k r may be viewed to be determined by the localized environment of the luminescent molecule. The localized environment perturbs the natural electronic configuration of the sensor molecule increasing the probability of its decay. The functional form of knr is determined by the nature of the interaction between the excited sensor and its surrounding perturbation. For example, the knr may be proportional to the concentration, partial pressure, or value of a [Parameter] of interest ... 

The nonradiative decay rate may also show some sort of saturation like in the case of diffusion controlled processes, in which the nonradiative events may be described, for example, by a Langmuir-like function... 

Consider, for example, a sensor composed of n phases each with a different nonradiative decay rate. The fraction of the excited sensor molecules Pi in phase ith may decay with an overall decay rate kr + k ri. In this case, the average probability of the sensor molecules of remaining in the excited state is given by... 

Figure 9.3. Stem-Volmer plot, based on luminescence intensity ratios, of heterogeneous sensor-carrier systems. In general, a straight lines are obtained when the dependence of the nonradiative decay rates for all phases are linear (Eq. (9.12)) regardless of the number of phases in the sensor-carrier preparation. Curvature is found when the value of the nonradiative decay rate knr does not increase proportionally with [parameter] (e.g., Eqs. (9.13, 9.14)).

In the case in which the overall sensor luminescence is the result of isolated phases each with a different nonradiative decay rate, the lifetimes of each phase provides an independent measurement of [Parameter]... 

The fluorescence and phosphorescence of luminescent materials are modulated by the characteristics of the environment to which these materials are exposed. Consequently, luminescent materials can be used as sensors (referred also as transducers or probes) to measure and monitor parameters of importance in medicine, industry and the environment. Temperature, oxygen, carbon dioxide, pH, voltage, and ions are examples of parameters that affect the luminescence of many materials. These transducers need to be excited by light. The manner in which the excited sensor returns to the ground state establishes the transducing characteristics of the luminescent material. It is determined by the concentration or value of the external parameter. A practical and unified approach to characterize the luminescence of all sensors is presented in this chapter. This approach introduces two general mechanisms referred as the radiative and the nonradiative paths. The radiative path, in the general approach, is determined by the molecular nature of the sensor. The nonradiative path is determined by the sensor environment, e.g., value or concentration of the external parameter. The nonradiative decay rate, associated with the nonradiative path, increases... 

The long lifetime has important consequences on the decay rates. First, we consider what affects the nonradiative rates (knr) which change the yields of fluorescence and phosphorescence. The nonradiative decay rate is often enhanced in molecules which have flexible constituents (the so-called loose-bolt effect). Therefore, both fluorescence and phosphorescence yields are generally larger for rigid molecules than flexible molecules. For the same reason, a rigid environment will increase the emission yields hence both fluorescence and phosphorescence yields often increase with increasing viscosity. 

Interaction between an Excited Electronic State and a Microsphere Radiative and Nonradiative Decay Rates... 

Conventional EPR techniques have been successfully used to measure the D and E values of matrix-isolated carbenes in the ground triplet state because the steady-state concentration of triplet species is sufficiently high in the system. The technique cannot be used, however, for excited species having triplet hfetimes of the order of 10-100 ns, since their steady-state concentration is too low. The D parameters are estimated from the external magnetic field effect on the T—T fluorescence decay in a hydrocarbon matrix at low temperamre. The method is based on the effect of the Zeeman mixing on the radiative and nonradiative decay rates of the T -Tq transition in the presence of a weak field. The D values are estimated by fitting the decay curve with that calculated for different D values. The D T ) values estimated for nonplanar DPC (ci symmetry) is 0.20... 

A similar but smaller intramolecular quenching effect was seen by Phillips and co-workers 44,4S) for 1-vinylnaphthalene copolymers incapable of excimer fluorescence. The monomer fluorescence lifetime of the 1-naphthyl group in the methyl methacrylate copolymer 44) was 20% less than the lifetime of 1-methylnaphthalene in the same solvent, tetrahydrofuran. However, no difference in lifetimes was observed between the 1-vinylnaphthalene/methyl acrylate copolymer 45) and 1-methylnaphthalene. To summarize, the nonradiative decay rate of excited singlet monomer in polymers, koM + k1M, may not be identical to that of a monochromophoric model compound, especially when the polymer contains quenching moieties and the solvent is fluid enough to allow rapid intramolecular quenching to occur. 

Study of the common situation in which there is no useful emission to use as a handle in kinetic analysis requires resourceful experimental programs. Measurement of the quantum yield of an A -> B reaction is of limited value, since quantum yields measure only the ratio of the nonradiative decay rates to A and B. Since both rates are expected to vary widely as a function of structure, the quantum yield alone tells next to nothing about the individual decay rates. The most popular approach to dissection of the kinetic problem involves the use of quenchers. Some third species, C, is introduced into the system in an attempt to intercept A. The most common interception process is energy transfer. 

The first systems without anomalous fluorescence discussed in the context of TICT states were coumarine laser dyes. Jones and coworkers208210 demonstrated that dialkylaminocoumarines like 7C showed an increase of the nonradiative decay rate in strongly polar solvents. This effect is dramatically increased if the acceptor properties of the coumarine skeleton are stronger, for example, in F7C. On the other... 

Marginal fluorescence quantum yields (1%) are generally observed though 25 and 33 fluorescence with 8% and 14% yields, respectively. Such low quantum yields are indicative of the effective competition of radiationless processes such as the Si —> Tj ISC and fast internal conversion (Si —> S0). The rate constants for radiative decay of Si (kF) range from 8 x 106 to 1.3 x 108 s-1, and the nonradiative decay rate constants (fcNR) range from 1.9 x 108 to 3.5 x 109 s / The nonradiative deactivation pathway is thus six times faster than the radiative one for 33 (anti) and about 110 times faster for 32 (syn). 

When decay curves were analyzed using a biexponential function, the nonradiative decay rate tsnr 1 of the slow component was evaluated by subtracting the radiative decay rate from the slow fluorescence decay rate. Figure 10 shows... 

Merkle et al. (1981) discussed three possible mechanisms of the pressure-enhanced decay rate an increase of the radiative decay rate of each Nd3+ ion, an increase of the nonradiative decay rate of each Nd3+ ion, or an increase in the interaction between Nd3+ ions leading to luminescence quenching. The nonradiative decay rates for the 4F3/2 multiplet were estimated to contribute less than 20% to the total decay rate (Powell et al., 1980) at ambient pressure. 

Table 2 S2-s0 Fluorescence Emission Parameters and Nonradiative Decay Rate...

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