Application of Smoluchowski's generalized theory to the kinetics of triplet–triplet annihilation of anthracene in viscous solution after long-pulse excitation

Abstract

The validity of Smoluchowski's theory is demonstrated by its application to the bimolecular triplet-triplet annihilation (TTA) T 1 þ T 1 ! S 0 þ S 1 in viscous solution. For that purpose the delayed S 1 ! S 0 fluorescence of anthracene in cis-1,3-dimethylcyclohexane/trans-1,4-dimethylcyclohexane (1:1) was measured after UV excitation with long laser pulses ($30 ms) in a temperature range where TTA is completely diffusion controlled. Through the adequate treatment of the kinetics of TTA upon spatially homogeneous and spatially periodic excitation (which is partially based on the results of previous publications) absolute values for the diffusion coefficients D of triplet molecules, for the effective annihilation distance R A and for the Fö rster radius R ST of heterogeneous annihilation S 1 þ T 1 ! S 0 þ T n were determined. The temperature dependence of all three parameters (D, R A and R ST ) is discussed. From the decrease of R A with increasing temperature, the parameters A and L can be determined, which define the exponential distance dependence of the annihilation of a triplet pair in the kinetic model of Butler and Pilling (1977). Differences of the two models and applicability criteria are discussed.

Optimizing photon upconversion by decoupling excimer formation and triplet triplet annihilation

“…[58][59][60][61] The effective interaction radius follows the Einstein-Smoluchowski relation (Note S1.7, ESI †), and can be calculated from eqn (5). 62,63 k TTA = 4pDNR TTA (5) where D is the molecular diffusion coefficient (eqn (S3), ESI †), and N is the Avogadro constant, R TTA is the effective TTA reaction radius. A large molecular size due to alkyl substitution reduces the mobility of annihilator molecules and also restricts the formation of an effective triplet pair by steric hindrance.…”

The Kinetics of Joined Action of Triplet-Triplet Annihilation and First-Order Decay of Molecules in the State in the Case of Nondominant First-Order Process

“…In Figure 2 there is an example of the result of fitting procedure: the decay of the delayed fluorescence of anthracene measured at 146 K, exited with the middle excitation pulse, presented in the plot parameters, obtained for nonexponential fit and are calculated from (17). Since results obtained with application of the simplified function defined by (18) have almost the same values they are omitted. The values of parameters obtained from nonexponential fit, are compared with the result of exponential approximation- (19).…”

“…P 4 will be called the indicator of nonexponential behavior. The condition P 4 ≤ 0.01 was used by Nickel and others [18,27] as a limit of dominant first-order decay in TTA kinetics.…”

“…In the case of triplet-triplet annihilation (TTA) in viscous solvents where the process takes place on microsecond timescale the deviations from diffusional Smoluchowski model [17] are not observed directly [18]. It means that the course of the intensity of delayed fluorescence as a function of time is well described by the function derived from Smoluchowski approach.…”

The Kinetics of Joined Action of Triplet-Triplet Annihilation and First-Order Decay of Molecules in T1State in the Case of Nondominant First-Order Process: The Kinetic Model in the Case of Spatially Periodic Excitation

“…Materials. e puri�cation of the materials: anthracene and cis-and transisomers of 2-methylcyclohexane (DMCH), as well the preparation of the sample was described in previous articles [7,11,18].…”