Stochastic Model of Photodynamics in Multichromophoric Conjugated Polymers

Abstract

A stochastic model of triplet exciton dynamics in multichromophoric conjugated polymers is presented and analyzed in detail, with a focus on the single molecule spectroscopy observables. The model deals with the evolution of a discrete statistical distribution of triplets in isolated polymer molecules. This approach should provide more accurate quantitative information on the dynamic processes involved, as compared to the previously used two-state model which assumes that a conjugated polymer cannot contain more than one triplet. In particular, it allows for determination of the triplet-triplet annihilation rate.

Population dynamics of multiple triplet excitons revealed from time-dependent fluorescence quenching of single conjugated polymer chains

“…The larger average quenching depths and faster quenching dynamics of P3HS SPCs are consistent with larger triplet occupancies and singlet-triplet quenching rates but, it is not possible to ascertain the relative magnitudes of associated rate constants by inspection alone. The former depend on triplet formation yields as well as the triplet and fluorescence lifetimes, however, it is not straightforward to directly infer relative contributions of triplet-triplet annihilation from I ( t )/ I (0) curves 41,46 .

Figure 2Experimental fluorescence quenching behavior of P3HS and P3HT comprised of ensemble averaged SPC data from a variable delay two-pulse approach recorded for various delay time intervals. Quenching dynamics are represented as I ( t )/ I (0) curves.

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“…Barzykin and Tachiya 41 had previously overcame the limitations imposed by assumptions of infinitely fast triplet-triplet annihilation by introducing an expanded stochastic photodynamic model to simulate the time-dependent evolution of multiple triplet populations from fluorescence intensity modulation data. Importantly, these authors only considered quenching behaviors from conjugated polymers with relatively low triplet yields (<10%) and, consequently, smaller populations of multiple triplet exciton configurations.…”

“…Importantly, these authors only considered quenching behaviors from conjugated polymers with relatively low triplet yields (<10%) and, consequently, smaller populations of multiple triplet exciton configurations. We now simulate population dynamics of multiple triplets and their interactions with emissive singlets by adopting a similar approach as Barzykin and Tachiya, which benefits from the fact that triplet decay kinetics are orders of magnitude slower than singlet decay time scales 41 . The model accounts for the existence of multiple chromophores where each can occupy either S 0 , S 1 or T 1 states at any given time where only the numbers of each state determine the overall configuration and not the specific location on the SPC 41 .…”

“…We now simulate population dynamics of multiple triplets and their interactions with emissive singlets by adopting a similar approach as Barzykin and Tachiya, which benefits from the fact that triplet decay kinetics are orders of magnitude slower than singlet decay time scales 41 . The model accounts for the existence of multiple chromophores where each can occupy either S 0 , S 1 or T 1 states at any given time where only the numbers of each state determine the overall configuration and not the specific location on the SPC 41 . The kinetic scheme for triplet formation and decay is given as follows for n triplets on an SPC that follows the same format as the original Smith-Ewart model,where k f , n is the forward rate constant for generating a triplet on an SPC with n triplets.…”

“…Quenching behavior is modeled by calculating the time-dependent probabilities of n = 0, 1, 2, … nth triplet population dynamics using a stochastic photodynamic model based on the Smith-Ewart differential difference equation originally developed to describe polymerization/emulsion kinetics 36–40 . We use the basic formalism of Barzykin and Tachiya 41 and employ the approach of Birtwistle and co-workers 39 to discretize and solve the Smith-Ewart model using the Gauss-Seidel iterative approach. Unlike effective two-state models mentioned earlier, this model incorporates finite triplet diffusion and triplet-triplet annihilation rate constants resulting in nonzero probabilities of multiple triplets at the SPC level.…”