How good is the generalized Langevin equation to describe the dynamics of photo-induced electron transfer in fluid solution?

The dynamics of unimolecular photo-triggered reactions can be strongly affected by the surrounding medium. An accurate description of these reactions requires knowing the free energy surface (FES) and the friction felt by the reactants. Most of theories start from the Langevin equation to derive the dynamics, but there are few examples comparing it with experiments. Here we explore the applicability of a Generalized Langevin Equation (GLE) with an arbitrary potential and a non-markovian friction. To this end we have performed broadband fluorescence measurements with sub-picosecond time resolution of a covalently linked organic electron donor-acceptor system in solvents of changing viscosity and dielectric permittivity. In order to establish the FES of the reaction we resort to stationary electronic spectroscopy. On the other hand, the dynamics of a non-reacting substance, Coumarin 153, provide the calibrating tool for the friction over the FES, which is assumed to be solute independent. A simpler and computationally faster approach uses the Generalized Smoluchowski Equation (GSE), which can be derived from the GLE for pure harmonic potentials. Both approaches reproduce the measurements in most of the solvents reasonably well. At long times, some differences arise from the errors inherited from the analysis of the stationary solvatochromism and at short times from the excess excitation energy. However, whenever the dynamics become slow the GSE shows larger deviations than the GLE, the results of which always agree qualitatively with the measured dynamics, regardless of the solvent viscosity or dielectric properties. The here applied method can be used to predict the dynamics of any other reacting system, given the FES parameters and solvent dynamics are provided. Thus no fitting parameters enter the GLE simulations, within the applicability limits found for the model in this work.Comment: 30 pages, 22 figures, 5 tables, 97 reference

Characterization of Dimethylsulfoxide / Glycerol Mixtures: A Binary Solvent System for the Study of "Friction-Dependent" Chemical Reactivity

The properties of binary mixtures of dimethylsulfoxide and glycerol, measured by several techniques, are reported. Special attention is given to those properties contributing or affecting chemical reactions. In this respect the investigated mixture behaves as a relatively simple solvent and it is especially well suited for studies on the influence of viscosity in chemical reactivity. This is due to the relative invariance of the dielectric properties of the mixture. However, special caution must be taken with specific solvation, as the hydrogen-bonding properties of the solvent changes with the molar fraction of glycerol.Comment: 49 pages including appendix, 20 figures and 89 reference

Towards efficient initiators for two-photon induced polymerization: Fine tuning of the donor/acceptor properties

In this work we present the design, synthesis and systematic investigation of the optical properties of symmetric triphenylamine (TPA)-substituted thiophenes. The use of electron-donating (-OMe, -tBu, -Me, -TMS), -neutral (-H) or -withdrawing (-F, -CN, -SO2Me) substituents gives rise to D-A-D based two-photon absorption (2PA) chromophores. The photophysical properties of these compounds, including one-photon absorption and 2PA using two-photon-excited fluorescence, were investigated in different organic solvents with varying polarity. The maximum 2PA cross sections prove to be strongly dependent on the nature of the TPA substituent and range between ~173 GM (Goeppert-Mayer units) and 379 GM. Although most of the investigated substances also exhibit high fluorescence quantum yields, two-photon absorption screening tests of an acrylate monomer formulation revealed the efficiency of these materials as 2PA photoinitiators. These results are supported by quantum chemical calculations of the spin density distribution indicating that the mechanism of polymerization initiation using acrylate monomer is favored by strong localization of the unpaired electrons in the triplet state on the C2 carbon of the thiophene moiety. © 2019 The Royal Society of Chemistry

Wavelength-optimized two-photon polymerization using initiators based on multipolar aminostyryl-1,3,5-triazines

Two-photon induced polymerization (2PP) based 3D printing is a powerful microfabrication tool. Specialized two-photon initiators (2PIs) are critical components of the employed photosensitive polymerizable formulations. This work investigates the cooperative enhancement of two-photon absorption cross sections (σ2PA) in a series of 1,3,5-triazine-derivatives bearing 1-3 aminostyryl-donor arms, creating dipolar, quadrupolar and octupolar push-pull systems. The multipolar 2PIs were successfully prepared and characterized, σ2PA were determined using z-scan at 800 nm as well as spectrally resolved two-photon excited fluorescence measurements, and the results were compared to high-level ab initio computations. Modern tunable femtosecond lasers allow 2PP-processing at optimum wavelengths tailored to the absorption behavior of the 2PI. 2PP structuring tests revealed that while performance at 800 nm is similar, at their respective σ2PA-maxima the octupolar triazine-derivative outperforms a well-established ketone-based quadrupolar reference 2PI, with significantly lower fabrication threshold at exceedingly high writing speeds up to 200 mm/s and a broader window for ideal processing parameters

Bimolecular photoinduced electron transfer reactions in liquids under the gaze of ultrafast spectroscopy

Because of their key role in many areas of science and technology, bimolecular photoinduced electron transfer reactions have been intensively studied over the past five decades. Despite this, several important questions, such as the absence of the Marcus inverted region or the structure of the primary reaction product, have only recently been solved while others still remain unanswered. Ultrafast spectroscopy has proven to be extremely powerful to monitor the entire electron transfer process and to access, with the help of state-of-the-art theoretical models of diffusion-assisted reactions, crucial information like e.g. the intrinsic charge separation dynamics beyond the diffusion limit. Additionally, extension of these experimental techniques to other spectral regions than the UV-visible, such as the infrared, has given a totally new insight into the nature, the structure and the dynamics of the key reaction intermediates, like exciplexes and ions pairs. In this perspective, we highlight these recent progresses and discuss several aspects that still need to be addressed before a thorough understanding of these processes can be attained

Driving Force Dependence of Charge Recombination in Reactive and Nonreactive Solvents

This study addresses the free energy dependence of charge recombination following photoinduced bimolecular electron transfer in three different solvents of either inert (acetonitrile and benzyl acetate) or reactive (N,N-dimethylaniline) character. Femtosecond time-resolved fluorescence and transient absorption have been used to determine the time scales for charge recombination. In pure N,N-dimethylaniline, charge recombination is found to be substantially slower than charge separation in a range of driving forces covering 1.5 eV. In all three solvents, the so-called Marcus inverted region is clearly observed for charge recombination. Additionally, the charge recombination step is found to be influenced by the solvent relaxation dynamics. A diffusion-reaction equation approach using an electron transfer model accounting for solvent relaxation is used to rationalize the experimental results

Bimolecular photo-induced electron transfer enlightened by diffusion

Photochemical electron transfer between freely diffusing molecules has been studied extensively. Here, we try to elucidate how much these works have contributed to the understanding of electron transfer. To this end, we have revisited the work performed in the experimental and theoretical areas of concern from the beginning of the 20th century up to the present day. We present a critical look at the major contributions and compile the current picture of a variety of phenomena around electron transfer in solution. This is based on two main developments, besides the theory of Marcus: encounter theories of diffusion and laser techniques in time-resolved spectroscopy

Model-free Investigation of Ultrafast Bimolecular Chemical Reactions: Bimolecular Photo Induced Electron Transfer

Using photoinduced bimolecular electron transfer reactions as example we demonstrate how diffusion controlled bimolecular chemical reactions can be studied in a model-free manner by quantitatively combining different ultrafast spectroscopical tools