Energy Conversion and Entropy Production in Biased Random Walk Processes-From Discrete Modeling to the Continuous Limit.

We considered discrete and continuous representations of a thermodynamic process in which a random walker (e.g., a molecular motor on a molecular track) uses periodically pumped energy (work) to pass N sites and move energetically downhill while dissipating heat. Interestingly, we found that, starting from a discrete model, the limit in which the motion becomes continuous in space and time (N→∞) is not unique and depends on what physical observables are assumed to be unchanged in the process. In particular, one may (as usually done) choose to keep the speed and diffusion coefficient fixed during this limiting process, in which case, the entropy production is affected. In addition, we also studied processes in which the entropy production is kept constant as N→∞ at the cost of a modified speed or diffusion coefficient. Furthermore, we also combined this dynamics with work against an opposing force, which made it possible to study the effect of discretization of the process on the thermodynamic efficiency of transferring the power input to the power output. Interestingly, we found that the efficiency was increased in the limit of N→∞. Finally, we investigated the same process when transitions between sites can only happen at finite time intervals and studied the impact of this time discretization on the thermodynamic variables as the continuous limit is approached.

A sensitive high repetition rate arrival time monitor for X-ray free electron lasers.

X-ray free-electron laser sources enable time-resolved X-ray studies with unmatched temporal resolution. To fully exploit ultrashort X-ray pulses, timing tools are essential. However, new high repetition rate X-ray facilities present challenges for currently used timing tool schemes. Here we address this issue by demonstrating a sensitive timing tool scheme to enhance experimental time resolution in pump-probe experiments at very high pulse repetition rates. Our method employs a self-referenced detection scheme using a time-sheared chirped optical pulse traversing an X-ray stimulated diamond plate. By formulating an effective medium theory, we confirm subtle refractive index changes, induced by sub-milli-Joule intense X-ray pulses, that are measured in our experiment. The system utilizes a Common-Path-Interferometer to detect X-ray-induced phase shifts of the optical probe pulse transmitted through the diamond sample. Owing to the thermal stability of diamond, our approach is well-suited for MHz pulse repetition rates in superconducting linear accelerator-based free-electron lasers.

Solvent Dynamics of Aqueous Halides before and after Photoionization.

Electron transfer reactions can be strongly influenced by solvent dynamics. We study the photoionization of halides in water as a model system for such reactions. There are no internal nuclear degrees of freedom in the solute, allowing the dynamics of the solvent to be uniquely identified. We simulate the equilibrium solvent dynamics for Cl-, Br-, I-, and their respective neutral atoms in water, comparing quantum mechanical/molecular mechanical (QM/MM) and classical molecular dynamics (MD) methods. On the basis of the obtained configurations, we calculate the extended X-ray absorption fine structure (EXAFS) spectra rigorously based on the MD snapshots and compare them in detail with other theoretical and experimental results available in the literature. We find our EXAFS spectra based on QM/MM MD simulations in good agreement with their experimental counterparts for the ions. Classical MD simulations for the ions lead to EXAFS spectra that agree equally well with the experiment when it comes to the oscillatory period of the signal, even though they differ from the QM/MM radial distribution functions extracted from the MD. The amplitude is, however, considerably overestimated. This suggests that to judge the reliability of theoretical simulation methods or to elucidate fine details of the atomistic dynamics of the solvent based on EXAFS spectra, the amplitude as well as the oscillatory period need to be considered. If simulations fail qualitatively, as does the classical MD for the aqueous neutral halogen atoms, the resulting EXAFS will also be strongly affected in both oscillatory period and amplitude. The good reliability of QM/MM-based EXAFS simulations, together with clear qualitative differences in the EXAFS spectra found between halides and their atomic counterparts, suggests that a combined theory and experimental EXAFS approach is suitable for elucidating the nonequilibrium solvent dynamics in the photoionization of halides and possibly also for electron transfer reactions in more complex systems.

Noise and thermodynamic uncertainty relation in "underwater" molecular junctions.

We determine the zero-frequency charge current noise in a metal-molecule-metal junction embedded in a thermal environment, e.g., a solvent, dominated by sequential charge transmission described by a classical master equation, and we study the dependence of specific model parameters, i.e., the environmental reorganization energy and relaxation behavior. Interestingly, the classical current noise term has the same structure as its quantum analog, which reflects a charge correlation due to the bridging molecule. We further determine the thermodynamic uncertainty relation (TUR) defininig a bound on the relationship between the average charge current, its fluctuation, and the entropy production in an electrochemical junction in the Marcus regime. In the second part, we use the same methodology to calculate the current noise and the TUR for a protoype photovoltaic cell in order to predict its upper bound for the efficiency of energy conversion into useful work.

Energy transfer and thermoelectricity in molecular junctions in non-equilibrated solvents.

We consider a molecular junction immersed in a solvent where the electron transfer is dominated by Marcus-type steps. However, the successive nature of the charge transfer through the junction does not imply that the solvent reaches thermal equilibrium throughout the transport. In our previous work [Kirchberg et al., J. Phys. Chem. Lett. 11, 1729 (2020)], we have determined the nonequilibrium distribution of the solvent where its dynamics, expressed by a friction, is considered in two limiting regimes of fast and slow solvent relaxation. In dependence of the nonequilibrium solvent dynamics, we investigate now the electrical, thermal, and thermoelectric properties of the molecular junction. We show that by suitable tuning of the friction, we can reduce the heat dissipation into the solvent and enhance the heat transfer between the electrodes. Interestingly, we find that the Seebeck coefficient grows significantly by adapting the solvent friction in both regimes.

Time-Resolved Probing of the Nonequilibrium Structural Solvation Dynamics by the Time-Dependent Stokes Shift.

The time-dependent fluorescence Stokes shift monitors the relaxation of the polarization of a polar solvent in the surroundings of a photoexcited solute molecule but also the structural variation of the solute following photoexcitation and the subsequent molecular charge redistribution. Here, we formulate a simple nonequilibrium quantum theory of solvation for an explicitly time-dependent continuous solvent. The time-dependent solvent induces nonequilibrium fluctuations on the solvent dynamics which are directly reflected in different time components in the time-dependent Stokes shift. We illustrate the structural dynamics in the presence of an explicitly time-dependent solvent by the example of a dynamically shrinking solute which leads to a bimodal Stokes shift. Interestingly, both contributions are mutually coupled. Furthermore, we can explain a prominent long-tail decay of the Stokes shift associated with slow structural dynamical variations.

Charge Transfer through Redox Molecular Junctions in Nonequilibrated Solvents.

Molecular conduction operating in dielectric solvent environments is often described using kinetic rates based on the Marcus theory of electron transfer at a molecule-metal electrode interface. However, the successive nature of charge transfer in such a system implies that the solvent does not necessarily reach equilibrium in such processes. Here we generalize the theory to account for solvent nonequilibrium and consider a molecular junction consisting of an electronic donor-acceptor system coupled to two metallic electrodes and placed in a polarizable solvent. We determine the nonequilbrium distribution of the solvent by solving diffusion equations in the strong- and weak-friction limits and calculate the charge current and its fluctuating behavior. In extreme limits, the absence of the solvent or fast solvent relaxation, the charge-transfer statistics is Poissonian, while it becomes correlated by the dynamic solvent between these limits. A Kramers-like turnover of the nonequilibrium current as a function of the solvent damping is found. Finally, we propose a way to tune the solvent-induced damping using geometrical control of the solvent dielectric response in nanostructured solvent channels.

Spectroscopic Signatures of the Dynamical Hydrophobic Solvation Shell Formation.

When a hydrophilic solute in water is suddenly turned into a hydrophobic species, for instance, by photoionization, a layer of hydrated water molecules forms around the solute on a time scale of a few picoseconds. We study the dynamic buildup of the hydration shell around a hydrophobic solute on the basis of a time-dependent dielectric continuum model. Information about the solvent is spectroscopically extracted from the relaxation dynamics of a test dipole inside a static Onsager sphere in the nonequilibrium solvent. The growth process is described phenomenologically within two approaches. First, we consider a time-dependent thickness of the hydration layer that grows from zero to a finite value over a finite time. Second, we assume a time-dependent complex permittivity within a finite layer region around the Onsager sphere. The layer is modeled as a continuous dielectric with a much slower fluctuation dynamics. We find a time-dependent frequency shift down to the blue of the resonant absorption of the dipole, together with a dynamically decreasing line width, as compared to bulk water. The blue shift reflects the work performed against the hydrogen-bonded network of the bulk solvent and is a directly measurable quantity. Our results are in agreement with an experiment on the hydrophobic solvation of iodine in water.