Concept of the Time-Dependent Diffusion Coefficient of Polarons in Organic Semiconductors and Its Determination from Time-Resolved Spectroscopy

Abstract

The population of photogenerated species in organic semiconductors may decay due to their mutual annihilation upon collisions during their diffusive motion. The standard kinetic models for the population decay, n(t), assume a time-invariant diffusion coefficient, i.e., D(t) ≡ constant. This leads to a failure in predicting the experimentally observed temporal evolution of photogenerated species if it asymptotically approaches a power-law decay n(t) ∼ t –x , with x < 0.5. We have used a concept of the time-dependent diffusion coefficient and developed a novel mathematical method of its determination from decay collision rates obtained by transient optical absorption spectroscopy. We tested the applicability of this method on the interpretation of data of the decay of polaron population obtained experimentally by time-resolved transient absorption measurements on thin films of regioregular poly­(3-hexylthiophene), where we recently reported a power-law asymptote with x = 0.24. While we do not assume any microscopic origin of the time variance of D(t), we argue that, as the charge-carrier trapping states occupancy drops with decaying charge concentration, the carrier motion slows down. This argument is supported by a recent report on a molecular-scale model taking into account significant local anisotropy present in linear conjugated polymers. Our concept can be applied for the description of the evolution of species, like polarons or excitons, in various organic materials, provided their decay kinetics is controlled by a mutual annihilation during one- or three-dimensional diffusion.

Impact of Hydrogen Bonds Limited Dipolar Disorder in High-k Polymer Gate Dielectric on Charge Carrier Transport in OFET

“…The dependences shown in Figure 7 were controlled by the level of the energy disorder σ as it has been theoretically demonstrated previously by the mobility dependences on the charge concentration (i.e., on the Fermi level) [46][47][48][49]. Interestingly, similar dependences as in Figure 7 were also found for the dependence of the diffusion coefficient of photogenerated polarons on their concentration in P3HT [51]. Due to higher dielectric constant at elevated temperature the markedly higher charge concentration was reached within the range of applied V SG voltage for OFETs with CEPVA50, particularly at temperatures above 50 • C. At higher temperatures the mobility decreases also began at higher by the level of the energy disorder charge concentration.…”

Kinetics of the Photoexcited States in Thin Films of Metallo-Supramolecular Polymers With Ditopic Thiophene-Bridged Terpyridine Ligands

“…For this case, we can relate the term from the right-hand side of Eq. 6 with the 1d time-dependent coefficient ( Menšík et al, 2018a ; Rais et al, 2018 ; Menšík et al, 2019 ) as or equivalently …”

“…Although the evolution of singlet and triplet exciton populations was experimentally well-characterized in the study by Rais et al, (2017b ), the origin of the bi-molecular singlet annihilation and subsequent triplet formation and decay remained unexplained. Meanwhile, we have elaborated a novel mathematical technique ( Menšík et al, 2018a ; Rais et al, 2018 ; Menšík et al, 2019 ), which makes the determination of the time-resolved diffusion coefficient from the transient absorption kinetics of photoexcited species possible. In this article, we applied the developed procedure on the previously acquired experimental data ( Rais et al, 2017b ) and proved that it is capable of elucidating in detail the process of the bi-molecular singlet annihilation and the subsequent formation and de-excitation of the triplet states.…”

Evolution of Diffusion Coefficient of Photoexcited Species in Excimer Forming Organic Thin Films

“…13 To cover these cases, a model with the timedependent diffusion coefficient of photoexcited species was applied recently. 14,15 It has been shown in these works how to reconstruct the time dependence of the diffusion coefficient of the photoexcited species from the time course of their timeresolved optical absorption if the process is controlled by the collision processes. The key point for this method is that the diffusion-controlled exciton annihilation can be described using the concept of the diffusion (heat) equation for a medium with a time-dependent diffusivity.…”

“…The key point for this method is that the diffusion-controlled exciton annihilation can be described using the concept of the diffusion (heat) equation for a medium with a time-dependent diffusivity. 14,15 This approach represents actually a phenomenological generalization of the microscopic kinetic models for the charge and excitation transport processes in organic semiconductors. The nature of this temporal variance can stem either from an explicit time dependence of the microscopic kinetic rates as was proved by the solution to quantum master equations 16−21 or from the dependence of charge carrier mobility on charge concentration due to the traps filling in disordered organic semiconductors.…”