Charge Transfer Rate Coefficients Research Articles

Dynamic electrochemical impedance spectroscopy for the charge transfer rate measurement of the ferro/ferricyanide redox couple on gold

• Rate coefficients of charge transfer are determined by dynamic EIS. • Rate coefficients are presented in a 0.2 V broad range. • By using dEIS, it is easier to preserve cleanliness of the system. • No a priori assumptions on potential dependences of rates are involved. The use of dynamic electrochemical impedance spectroscopy, dEIS is shown in the context of diffusion-controlled electrode reactions. By this method, a number of audio-frequency impedance spectra were measured on a gold electrode in an aqueous solution of K 4 [Fe(CN) 6 ] while taking cyclic voltammograms (the CVs were taken with 50–200 mV/s scan-rate; the distance of potentials of impedance spectra was 16 mV). The Faradaic impedance elements were determined from the spectra, from them charge transfer rate coefficients were calculated; it was found to be 0.11 cm/s at the formal potential. This set of measurements demonstrates the main advantage of dEIS over the traditional steady state impedance measurements: dEIS characterization of an electrochemical system can be performed in seconds rather than minutes which makes possible to use freshly prepared (e.g., annealed) electrodes with reduced risk of contamination or modification of their surfaces.

Linear-Response and Nonlinear-Response Formulations of the Instantaneous Marcus Theory for Nonequilibrium Photoinduced Charge Transfer.

Instantaneous Marcus theory (IMT) offers a way for capturing the time-dependent charge transfer (CT) rate coefficient in nonequilibrium photoinduced CT processes, where the system was photoexcited from its equilibrated ground state vertically to the excitonic state, followed by an electronic transition to the CT state. As derived from the linearized semiclassical nonequilibrium Fermi's golden rule (LSC NE-FGR), the original IMT requires expensive all-atom nonequilibrium molecular dynamics (NEMD) simulations. In this work, we propose computationally efficient linear-response and nonlinear-response formulations for IMT rate calculations, which only require equilibrium molecular dynamics simulations. The linear- and nonlinear-response IMT methods were tested to predict the transient behavior in the photoinduced CT dynamics of the carotenoid-porphyrin-C60 molecular triad solvated in explicit tetrahydrofuran. Our result demonstrated that the nonlinear-response IMT is in excellent agreement with the benchmark NEMD for all cases investigated here, whereas the linear-response IMT predicts the correct trend for all cases but overestimates the transient CT rate in one case involving a significant nonequilibrium relaxation. This mild breakdown of linear-response IMT is due to neglecting the higher-order terms in the exact nonlinear-response IMT. Taking advantage of time translational symmetry, the linear- and nonlinear-response approaches were demonstrated to be able to reduce the computational cost by 80% and 60% compared with NEMD simulations, respectively. Thus, we highly recommend the readily applicable and accurate nonlinear-response IMT approach for simulating nonequilibrium CT processes in complex molecular systems in the condensed phase.

Redox chemistry of nitrogen-doped CNT-encapsulated nitroxide radical polymers for high energy density and rate-capability organic batteries

To enhance the electrochemical performance and identify the redox reaction of a nitroxide radical-based organic battery, poly(2,2,6,6-tetramethylpiperidinyloxy-4-vinylmethacrylate) (PTMA) as nitroxide radical polymer is synthesized and used to fill the central pore of nitrogen-doped carbon nanotubes (NCNTs). The PTMA-filled NCNTs demonstrate high rate capability, stable cycling, and high electrode stability, owing to their high charge transfer and ion diffusion; further, they prevent the dissolution of organic active material. The nitrogen doping on CNTs improves the electrochemical properties by created defects. The PTMA-filled NCNT cells have a high reversible capacity of 199.8 mAh g−1 and high energy density of 489.4 Wh kg−1 on electrode level at 0.2C with a two-step redox couple. Moreover, the cells with the two-step redox couple exhibit excellent stable cycle performance with high capacity retention and Coulombic efficiency for 3000 cycles. The nitroxide radical of PTMA can be converted to either an oxoammonium cation or an aminoxy anion; further, the redox reaction of each step exhibits different performance. The nitroxide radical–oxoammonium cation redox step in NCNTs shows a high rate capability owing to the high charge transfer rate and ion diffusion coefficient. The unusual results will help further improve the properties and commercialization of rechargeable organic batteries.

Photoinduced Charge Transfer Dynamics in the Carotenoid-Porphyrin-C60 Triad via the Linearized Semiclassical Nonequilibrium Fermi's Golden Rule.

The nonequilibrium Fermi's golden rule (NE-FGR) describes the time-dependent rate coefficient for electronic transitions when the nuclear degrees of freedom start out in a nonequilibrium state. In this paper, the linearized semiclassical (LSC) approximation of the NE-FGR is used to calculate the photoinduced charge transfer (CT) rates in the carotenoid-porphyrin-C60 molecular triad dissolved in explicit tetrahydrofuran. The initial nonequilibrium state corresponds to impulsive photoexcitation from the equilibrated ground state to the ππ* state, and the porphyrin-to-C60 and carotenoid-to-C60 CT rates are calculated. Our results show that accounting for the nonequilibrium nature of the initial state significantly enhances the transition rate of the porphyrin-to-C60 CT process. We also derive the instantaneous Marcus theory (IMT) from LSC NE-FGR, which casts the CT rate coefficients in terms of a Marcus-like expression, with explicitly time-dependent reorganization energy and reaction free energy. IMT is found to reproduce the CT rates in the system under consideration remarkably well.

Dynamic electrochemical impedance spectroscopy of quasi-reversible redox systems. Properties of the Faradaic impedance, and relations to those of voltammograms

By analysing the electrochemical impedance spectra (EIS) of quasi-reversible redox systems, the two elements of the Faradaic impedance: charge transfer resistance and the coupled Warburg-coefficient can be obtained at a given potential. The same applies also to DEIS (dynamic EIS) measurements, when high frequency impedance spectra are measured while the potential is scanned to simultaneously accomplish cyclic voltammetry or other transient measurements. In case of DEIS both the charge transfer resistance and the Warburg coefficient depend on the applied potential program, e.g. on scan-rate. A theory is presented, yielding a transformation by which this dependence can be eliminated. The proposed procedure yields two, scan-rate independent, hysteresis-free functions, which are closely related to the EIS results, and also to the functions which are the transformed forms of the cyclic voltammograms as suggested in T. Pajkossy, S. Vesztergom, Electrochim. Acta,297 (2019) 1121. To illustrate the properties of the transformations and the functions involved, numerical simulations are also presented. The theory opens a new route for the high-accuracy, fast determination of charge transfer rate coefficients of quasi-reversible redox systems by employing DEIS.

Analysis of voltammograms of quasi-reversible redox systems: Transformation to potential program invariant form

A simple procedure has recently been suggested (T. Pajkossy, Electrochem. Comm.90 (2018) 69) by which various types of voltammograms, above all cyclic voltammograms, pertaining to partially diffusion controlled charge transfer reactions can be analysed. Using this procedure, from voltammograms taken with varied scan-rates or other-than-triangular waveforms two scan-rate independent, hysteresis-free functions can be calculated. One of them is the diffusion-free polarization curve; the other the semiintegrated form of the reversible voltammograms. Here we show the underlying theory in details, along with numerical simulations to highlight important properties of the transformation. The theory opens a new route for the determination of charge-transfer rate coefficients of quasi-reversible redox systems.

Increase of the Charge Transfer Rate Coefficients for NO+ and O2+• Reactions with Isoprene Molecules at Elevated Interaction Energies

Atmospheric concentrations of isoprene (2-methylbutadiene) in environmental research and in exhaled breath for medical research are usually measured by soft chemical ionization mass spectrometry that relies on a knowledge of the kinetics of the gas phase reactions of H3O+, NO+ or O2+• ions with isoprene molecules. Thus, we have carried out an experimental study of the rate coefficients, k, and product ions distributions for such reactions over a range of ion-molecule interaction energy, Er, (0.05-0.8 eV) in a helium-buffered selected ion flow-drift tube, SIFDT. It is found that contrary to the ion-induced dipole capture model, k for the NO+ and O2+• charge transfer reactions almost doubled over the E r range, while k for the H3O+ proton transfer reaction did not significantly change with E r, as predicted. These results reveal that the reaction mechanism involving ion-molecule capture forming an intermediate complex does not properly describe charge transfer to isoprene molecules. It is important to account for this increase in k with E r in these isoprene charge transfer reactions, and probably for other such reactions, when using drift tube reactors for trace gas analysis.

Radiative Charge Transfer between the Helium Ion and Argon

Abstract The rate coefficient for radiative charge transfer between the helium ion and an argon atom is calculated. The rate coefficient is about at 300 K in agreement with earlier experimental data.

Measurement of ionization, attachment, detachment and charge transfer rate coefficients in dry air around the critical electric field

We obtain pressure-dependent rate coefficients in dry synthetic air (79% , 21% ) by fitting Pulsed Townsend measurements over a pressure range from 10 to 100 kPa, around the critical density-reduced electric field from 86 to 104 Td. The physical processes are reviewed and set in relation to a suitable kinetic model. A procedure for fitting kinetic reaction rates, based on finite-volume simulations of charge carrier drift, is described. Rate coefficients are obtained for electron attachment, ionization and detachment, as well as for ion conversion. We find a quadratic pressure dependency in the conversion rate, consistent with three-body collisions, and observe a pressure dependency in the onset of electron avalanche growth in dry air.

Radiative charge transfer in collisions of C with He+

Radiative charge exchange collisions between a carbon atom and a helium ion , both in their ground state, are investigated theoretically. Detailed quantum chemistry calculations are carried out to obtain potential energy curves and transition dipole matrix elements for doublet and quartet molecular states of the HeC+ cation. Radiative charge transfer cross sections and rate coefficients are calculated and are found at thermal and lower energies to be large compared to those for direct charge transfer. The present results might be applicable to modelling the complex interplay of (or ), , and at the boundaries of interstellar photon dominated regions and in x-ray dominated regions, where the abundance of affects the abundance of .

Charge transfer of 3He2 + with H2, CH4, N2 and CO at energies below 1 eV

We report our measured values for the sum of single and double charge transfer rate coefficients between 3He2 + and H2, CH4, N2 and CO. Our values are 2.4 ± 0.2 × 10−9 cm3 s−1 for H2, 6.3 ± 0.9 × 10−9 cm3 s−1 for CH4, 4.0 ± 0.3 × 10−9 cm3 s−1 for N2 and 4.7 ± 0.4 × 10−9 cm3 s−1 for CO. The values are obtained at equivalent temperatures of 1200–2400 K.

Resonant charge transfer of 3He2 + with 4He(1s2) at energies below 1 eV

The rate coefficient of resonant charge transfer between 3He2 + and 4He, at energies below 1 eV, was measured using an rf ion trap and time-of-flight mass spectrometry. We obtain a resonant charge transfer rate coefficient of 5.9 ± 0.6 × 10−10 cm3 s−1 at an equivalent temperature of 1200 K. The measured value compares favourably to existing calculations. This measurement extends our knowledge to a broader spectrum of energies as it provides information on the rate coefficients at a low energy and adds to our understanding of the charge transfer process of 3He2 +, α-particles, with He encountered in astrophysics and nuclear fusion.

Nonradiative charge transfer in collisions of protons with rubidium atoms

The nonradiative charge-transfer cross sections for protons colliding with Rb(5s) atoms are calculated by using the quantum-mechanical molecularorbital close-coupling method in an energy range of 10−3 keV–10 keV. The total and state-selective charge-transfer cross sections are in good agreement with the experimental data in the relatively low energy region. The importance of rotational coupling for chargetransfer process is stressed. Compared with the radiative charge-transfer process, nonradiative charge transfer is a dominant mechanism at energies above 15 eV. The resonance structures of state-selective charge-transfer cross sections arising from the competition among channels are analysed in detail. The radiative and nonradiative charge-transfer rate coefficients from low to high temperature are presented.

Isotope effect in charge-transfer collisions of H with He+

We present a theoretical study of the isotope effect arising from the replacement of H by T in the charge-transfer collision H(n=2) + He{sup +}(1s) at low energy. Using a quasimolecular approach and a time-dependent wave-packet method, we compute the cross sections for the reaction including the effects of the nonadiabatic radial and rotational couplings. For H(2s) + He{sup +}(1s) collisions, we find a strong isotope effect at energies below 1 eV/amu for both singlet and triplet states. We find a much smaller isotopic dependence of the cross section for H(2p) + He{sup +}(1s) collisions in triplet states, and no isotope effect in singlet states. We explain the isotope effect on the basis of the potential energy curves and the nonadiabatic couplings, and we evaluate the importance of the isotope effect on the charge-transfer rate coefficients.

Atomic data for neutron-capture elements

We present total and final-state resolved charge transfer (CT) rate coefficients for low-charge Ge, Se, Br, Kr, Rb, and Xe ions reacting with neutral hydrogen over the temperature range 10^2--10^6 K. Each of these elements has been detected in ionized astrophysical nebulae, particularly planetary nebulae. CT rate coefficients are a key ingredient for the ionization equilibrium solutions needed to determine total elemental abundances from those of the observed ions. A multi-channel Landau Zener approach was used to compute rate coefficients for projectile ions with charges q=2-5, and for singly-charged ions the Demkov approximation was utilized. Our results for five-times ionized species are lower limits, due to the incompleteness of level energies in the NIST database. In addition, we computed rate coefficients for charge transfer ionization reactions between the neutral species of the above six elements and ionized hydrogen. The resulting total and state-resolved CT rate coefficients are tabulated and available at the CDS. In tandem with our concurrent investigations of other important atomic processes in photoionized nebulae, this work will enable robust investigations of neutron-capture element abundances and nucleosynthesis via nebular spectroscopy.

Atomic data for neutron-capture elements

We present multi-configuration Breit-Pauli distorted-wave photoionization (PI) cross sections and radiative recombination (RR) and dielectronic recombination (DR) rate coefficients for the first six krypton ions. These were calculated with the AUTOSTRUCTURE code, using semi-relativistic radial wavefunctions in intermediate coupling. Kr has been detected in several planetary nebulae (PNe) and H II regions, and is a useful tracer of neutron-capture nucleosynthesis. PI, RR, and DR data are required to accurately correct for unobserved Kr ions in ionized nebulae, and hence to determine elemental Kr abundances. PI cross sections have been determined for ground configuration states of Kr^0--Kr^5+ up to 100 Rydbergs. Our Kr^+ PI calculations were significantly improved through comparison with experimental measurements. RR and DR rate coefficients were determined from the direct and resonant PI cross sections at temperatures (10^1--10^7)z^2 K, where z is the charge. We account for Delta n=0 DR core excitations, and find that DR is the dominant recombination mechanism for all but Kr^+ at photoionized plasma temperatures. Internal uncertainties are estimated by comparing results computed with three different configuration-interaction expansions for each ion, and by testing the sensitivity to variations in the orbital radial scaling parameters. The PI cross sections are generally uncertain by 30-50% near the ground state thresholds. Near 10^4 K, the RR rate coefficients are typically uncertain by <10%, while those of DR exhibit uncertainties of factors of 2 to 3, due to the unknown energies of near-threshold autoionizing resonances. With the charge transfer rate coefficients presented in the third paper of this series, these data enable robust Kr abundance determinations in photoionized nebulae for the first time.

Advances in atomic data for neutron-capture elements

AbstractNeutron(n)-capture elements (atomic number Z &gt; 30), which can be produced in planetary nebula (PN) progenitor stars via s-process nucleosynthesis, have been detected in nearly 100 PNe. This demonstrates that nebular spectroscopy is a potentially powerful tool for studying the production and chemical evolution of trans-iron elements. However, significant challenges must be addressed before this goal can be achieved. One of the most substantial hurdles is the lack of atomic data for n-capture elements, particularly that needed to solve for their ionization equilibrium (and hence to convert ionic abundances to elemental abundances). To address this need, we have computed photoionization cross sections and radiative and dielectronic recombination rate coefficients for the first six ions of Se and Kr. The calculations were benchmarked against experimental photoionization cross section measurements. In addition, we computed charge transfer (CT) rate coefficients for ions of six n-capture elements. These efforts will enable the accurate determination of nebular Se and Kr abundances, allowing robust investigations of s-process enrichments in PNe.

New atomic data for trans-iron elements and their application to abundance determinations in planetary nebulae1This review is part of a Special Issue on the 10th International Colloquium on Atomic Spectra and Oscillator Strengths for Astrophysical and Laboratory Plasmas.

Investigations of neutron(n)-capture element nucleosynthesis and chemical evolution have largely been based on stellar spectroscopy. However, the recent detection of these elements in several planetary nebulae (PNe) indicates that nebular spectroscopy is a promising new tool for such studies. In PNe, n-capture element abundance determinations reveal details of s-process nucleosynthesis and convective mixing in evolved low-mass stars, as well as the chemical evolution of elements that cannot be detected in stellar spectra. Only one or two ions of a given trans-iron element can typically be detected in individual nebulae. Elemental abundance determinations thus require corrections for the abundances of unobserved ions. Such corrections rely on the availability of atomic data for processes that control the ionization equilibrium of nebulae (e.g., photoionization cross sections and rate coefficients for various recombination processes). Until recently, these data were unknown for virtually all n-capture element ions. For the first six ions of Se, Kr, and Xe — the three most widely detected n-capture elements in PNe — we are calculating photoionization cross sections and radiative and dielectronic recombination rate coefficients using the multi-configuration Breit–Pauli atomic structure code AUTOSTRUCTURE. Charge transfer rate coefficients are being determined with a multichannel Landau–Zener code. To calibrate these calculations, we have measured absolute photoionization cross sections of Se and Xe ions at the Advanced Light Source synchrotron radiation facility. These atomic data can be incorporated into photoionization codes, which we will use to derive ionization corrections (hence abundances) for Se, Kr, and Xe in ionized nebulae. Using Monte Carlo simulations, we will investigate the effects of atomic data uncertainties on the derived abundances, illuminating the systems and atomic processes that require further analysis. These results are critical for honing nebular spectroscopy into a more effective tool for investigating the production and chemical evolution of trans-iron elements in the Universe.

Charge transfer rate coefficients in collision of C2+ ions with CO and N2 molecular targets

An ab initio molecular treatment of the charge transfer process in collision of C2+ ions with the isoelectronic CO and N2 targets has been performed. The corresponding rate coefficients in the 400–50000K temperature range are compared to recent measurements of Gao and Kwong at Tequiv=1.17×104K. A global satisfactory agreement is observed and some general behaviour may be deduced.

Charge transfer and association of protons colliding with potassium from very low to intermediate energies

The nonradiative charge-transfer process for ${\mathrm{H}}^{+}+\mathrm{K}(4s)$ collision is investigated using the quantum-mechanical molecular-orbital close-coupling method for collision energies from $1$ eV to $10$ keV. The radiative-decay and radiative charge transfer cross sections are calculated using the optical potential approach and the fully quantal method, respectively, for the energy range of ${10}^{\ensuremath{-}5}$--$10$ eV. The radiative-association cross sections are obtained by subtracting the radiative charge-transfer part from total radiative-decay cross sections. The relevant molecular data are calculated from the multireference single- and double-excitation configuration interaction approach. The nonradiative charge transfer is the dominant mechanism at energies above $2$ eV, whereas the radiative charge transfer becomes primary in the low-energy region of $El1.5$ eV. The present radiative-decay cross sections disagree with the calculations of Watanabe et al. [Phys. Rev. A 66, 044701 (2002)]. The total charge-transfer rate coefficient is obtained in the temperature range of $1$--$20$$000$ K.