Rate constant nonradiative

The effect of the substitution of a heavy-atom directly onto the nucleus of aromatic compounds (internal heavy-atom effect) on intercombinational radiative and nonradiative processes can be seen by examination of experimental data obtained for naphthalene and its derivatives. The data obtained by Ermolaev and Svitashev<104) and analyzed by Birks(24) to obtain individual rate constants for the various processes are collected in Table 5.9. 

It has been possible to employ the heavy-atom solvent effect in determining the rate constants for the various intercombinational nonradiative transitions in acenaphthylene and 5,6-dichIoroacenaphthylene.<436,c,rate constants, which are not accessible in light-atom solvents due to the complexity of the mechanism and the low efficiency of intersystem crossing from the first excited singlet to the first excited triplet, can be readily evaluated under the influence of heavy-atom perturbation. 

In the limit that Huty >> kgT, the rate constant for nonradiative decay is simply the product of the square of the vibrational overlap integral and an electronic term for the... 

Figure 9.1. Radiative and nonradiative paths to the ground state of excited sensor molecules m. All possible mechanisms by which an excited molecule may return to the ground state are sorted in two sets. One set, characterized by the rate constant kr, is referred as the radiative path. The second set, characterized by the rate function knr, is referred to in this chapter as the nonradiative path.

Nonradiative processes (knr) can occur with a wide range of rate constants. Molecules with high knr values display low quantum yields due to rapid depopulation of the excited state by this route. The measured lifetime in the absence of collisional or energy transfer quenching is usually referred to as To, and is given by to = (kr + knr). ... 

Fig. 27. Semilogarithmic plot of the nonradiative triplet rate constant against (E— o)/> for the normal and deuterated hydrocarbons listed in Ref. t)). The broken line, derived from phosphorescence spectra, is taken from Ref. t). The slopes of the two solid lines differ by a factor 1.35. (O.Ci-jjH, E = 4000 cm l 0 Ci fl Z>u, =5500 cm t). The following totally deuterated hydrocarbons are included benzene, triphenylene, acenaphtene, naphthalene, phenanthrene, chrysene, biphenyl, p-terphenyl, pyrene, 1,2-benzanthracene, anthracene (in the order of increasing /S). (From Siebrand and Williams, Ref. l)...

The further assumption that 3M is degenerate with the correlating molecular triplet state 3M provides an estimate of the energy (3M ) of this state in the region (XM ) > (3M ) > E(3M ) which may be spectroscopically inaccessible. Double intersystem crossing to different molecular triplet states of naphthalene87 is also apparently exhibited by the excimer of 1,6-dimethylnaphthalene40 in which the nonradiative process is characterized by a rate constant kf which is the sum of temperature-dependent and temperature-independent terms. The value of the latter is also consistent with a spin-prohibited process (Table XVI). 

Fig. 34 Photosensitized singlet oxygen production 1/ r is the general (radiative and non-radiative) rate constant of the transition Si So fcsi is the rate constant of singlet-triplet conversion tt is the lifetime of the triplet, T1, electronic state of PS kj is the second-order rate constant of singlet oxygen quenching of the Ti state of PS tl and nr are the radiative lifetime and rate constant of all intramolecular nonradiative energy relaxation processes of O2 ( Ag)...

These discussions provide an explanation for the fact that fluorescence emission is normally observed from the zero vibrational level of the first excited state of a molecule (Kasha s rule). The photochemical behaviour of polyatomic molecules is almost always decided by the chemical properties of their first excited state. Azulenes and substituted azulenes are some important exceptions to this rule observed so far. The fluorescence from azulene originates from S2 state and is the mirror image of S2 S0 transition in absorption. It appears that in this molecule, S1 - S0 absorption energy is lost in a time less than the fluorescence lifetime, whereas certain restrictions are imposed for S2 -> S0 nonradiative transitions. In azulene, the energy gap AE, between S2 and St is large compared with that between S2 and S0. The small value of AE facilitates radiationless conversion from 5, but that from S2 cannot compete with fluorescence emission. Recently, more sensitive measurement techniques such as picosecond flash fluorimetry have led to the observation of S - - S0 fluorescence also. The emission is extremely weak. Higher energy states of some other molecules have been observed to emit very weak fluorescence. The effect is controlled by the relative rate constants of the photophysical processes. 

Rate constants for nonradiative steps are difficult to obtain experimentally. The quantum yield for intersystem crossing is expressed as... 

The expression for rate constant for transfer is similar to the one derived for nonradiative processes within a molecule... 

The actual lifetime T of an excited molecule is usually less than xr because of the competing nonradi-ative processes. The sum of their rate constants can be designated /cnr. The fluorescence efficiency (or quantum yield) ( )F is given by Eq. 23-15. 

The rate of relaxation by nonradiative pathways can be increased by addition of quenchers. Quenching of fluorescence occurs by several mechanisms, many of which involve collision of the excited chro-mophore with the quenching molecule. Some substances such as iodide ion are especially effective quenchers. The fluorescence efficiency of a substance in the absence of a quencher can be expressed (Eq. 23-lb) in terms of the rate constants for fluorescence (fcf), for nonradiative decay (km), and for phosphorescence ( r )=... 

One further case should be examined. Suppose that in equation (9), Q is formed and is chemically reactive, going to product P with a rate constant k CT. In addition, Q will have rate constants k nr and k r for nonradiative and radiative relaxation, respectively. The situation is now that light is absorbed by A, but we measure the formation of product P. We speak of such a process as one of sensitization, that is, the formation of P is photosensitized by A. 

Adams and Cherry (78) have investigated the effects of stilbene substitution on the behavior of their excited complexes with fumaronitrile and find that the rate constants for fluorescence and nonradiative decay are insensitive to substitution, but that the rate constant for intersystem crossing is increased by electron-donating substituents (lower stilbene oxidation potential). This trend is attributed to a decrease in the energy gap between the excited complex and locally excited 3t (Fig. 4). The observed energy gap dependence of the exciplex lifetime could also account for the absence of fluorescence (or cycloadduct formation, see Section IV-B) from the excited charge-transfer complexes of t-1 with stronger electron acceptors such as maleic anhydride (76) or tetracyanoethylene (85). 

Irradiation of t-1 with fumaronitrile in polar solvents results in the formation of a nonfluorescent radical ion pair which decays via intersystem crossing to locally excited t with a quantum yield of 1.0 (88). The rate constant for nonradiative decay of the radical ion pair increased with increasing solvent polarity (89). Dissociation of the ion pair competes inefficiently with intersystem crossing and yields the cation radical of t-1, which has been observed and characterized by time resolved resonance Raman (TR ) (88) and transient absorption spectroscopy (89). The strongest feature in the TR ... 

The lowest vibrational energy levels of a state are indicated by thick horizontal lines other horizontal lines represent associated vibrational levels. Vertical straight lines represent radiative transitions, wavy lines nonradiative transitions. The orders of magnitude of the first-order rate constants for the various processes are indicated. From R. B. Gundall and A. Gilbert, Photochemistry, Thomas Nelson, London, 1970. Reproduced by permission of Thomas Nelson and Sons Limited. 

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). 

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