Diffusion Coefficient Of Charge Carriers Research Articles

Decoupling Reaction, Diffusion and Ohmic Processes in Fast-Charging Electrodes: A New Model for CV Data Analysis

Fast charging is critical for the efficient storage of energy in devices like electric vehicles and portable electronics. The rate performance of electrodes is limited by the electron transfer rate, the ohmic resistance of the electrode, the size and shape of the primary electrode particles, and the charge carrier diffusion process within the electrodes. However, separating the intrinsic contributions of mass transport and charge transfer from non-equilibrium data obtained under large interfacial polarization is very complex, which limits our understanding of high rate electrodes during charging and discharging. While it is possible to extract the diffusive and capacitive components of an electrode’s capacity from cyclic voltammetry (CV) data using the Dunn method, the Dunn model assumes a constant diffusional overpotential. In reality the ohmic resistance scales with the current, so that the ohmic potential drop across the electrode cannot be neglected a priori for fast charging electrodes in which high current densities are a requirement.We recently developed a new model based on the Butler-Volmer equation for the kinetics of the electron exchange process, and incorporated the charge carrier diffusion process and the internal ohmic losses, as well as the effect of the shape and dimensions of the primary electrode particles on the effective diffusion rate [1]. The model can provide the relation between current peak voltages and peak currents from a series of sweep rate CV measurements. The ohmic resistance, equilibrium voltage, exchange current (related to the electrochemical reaction rate) and limiting current (related to the charge carrier diffusion coefficient and Nernst diffusion layer thickness) can be extracted as independent variables from the fitted experimental data.By simulating a range of different high rate Li electrode materials (both cathodes and anodes), we identified influence of the reaction rate on the overpotential as a common significant factor, which explains the nonlinear relation between the potential and the current at peak position in different CV measurements. Our analysis suggests that a higher electrochemical reaction rate seems to be more important for the realization of faster charging batteries than a larger carrier diffusion coefficient.Finally, our extended model also enables us to predict the overpotential at any applied potential, which is not possible with other current models known till date. This insight helps us to gain more detailed understanding of the relationship between the intrinsic properties of the electrode materials and their rate performance in different reaction stages. This may facilitate further modification of electrode material towards enhanced high rate performance in next-generation batteries.[1] R. Xia et al., Energy Storage Mater. 53 (2022) 381-390.

Determination of transport properties for polymer electrolytes containing LiTf and MgTf2 salts

Solid polymer electrolytes were prepared using polymethyl methacrylate (PMMA), ethylene carbonate (EC), lithium trifluoroethane-sulfonate (LiTf), magnesium trifluoro-methanesulfonate (MgTf2). The ionic conductivity was measured at 30 °C as 6.17 × 10−6 and 1.83 × 10−4 S cm−1, respectively. The ionic mobility (μ), charge carrier diffusion coefficient (D) and the ion number density (n) of the samples have been calculated to understand the effect of these parameters on the ionic conductivity. The experimentally obtained values of and are compared with theoretical calculations. The PMMA-EC-MgTf2 sample exhibits higher dielectric constant compared to PMMA-EC-LiTf. The MgTf2 containing sample also exhibits a higher transference number.

Diffusion coefficient of charge carriers in disordered semiconductors retaining a combination of exponential and Gaussian mobility-gap states: Application to amorphous selenium

Charge carrier transport in disordered semiconductors is highly influenced by the defect states near the mobility edges. A theoretical model for the generalized Einstein relation, namely, the diffusivity-mobility ratio, for disordered semiconductors retaining a combination of exponential and Gaussian mobility-gap states with square-root distribution of extended states, is presented in this article. The conditions for determining the diffusion coefficient of charge carriers in disordered semiconductors from the Einstein relation are described in the article. The effects of various parameters constituting the density of states (DOS) distribution on the Einstein relation are examined. The results show that the diffusivity-mobility ratio for such DOS distribution substantially deviates from the traditional constant value for carrier concentration larger than 1010 cm−3. The value of diffusivity-mobility ratio strongly depends on the amount, energy position, and the shape of the Gaussian peaks. The additional diffusion coefficient due to multiple trapping in disordered semiconductors (namely, field diffusion) under quasi-equilibrium transport is also examined as a function of electric field and carrier concentration.

INFLUENCE OF STRUCTURAL FEATURES OF ZNO FILMS ON OPTICAL AND PHOTOELECTRIC CHARACTERISTICS OF INVERTED POLYMER SOLAR ELEMENTS

In this work we investigated the effect of preliminary annealing of zinc acetate solution films on the morphology, structure, optical properties of the formed ZnO films and also on the photovoltaic properties of polymer solar cells based on the obtained ZnO films. It was found that the pre-annealing temperature significantly affects the morphology and structure of the obtained ZnO films. At pre-annealing temperatures below 200 oC the films have a strongly relief morphology (wrinkled morphology), while at pre-annealing temperatures above 200 oC the surface morphology of the films is smooth. The relief of ZnO films affects the photocurrent density of solar cells. Cells based on ZnO films with wrinkled morphology showed a higher photocurrent compared to smooth morphology, which is due to strong light scattering and, as a result, the optical path of light in the photoactive layer is increased due to multiple reflection of light in the wrinkled structure of ZnO. In addition, with increasing pre-annealing temperature, the photovoltage of solar cells and the rate of recombination of charge carriers increases, but the diffusion coefficient of charge carriers decreases, which indicates an increase in the density of defects in the crystal lattice of ZnO. Thus, it has been shown that smooth or highly relief thin ZnO films with controlled properties can be obtained from a zinc acetate solution.

In Ukrainian

The paper presents a system of equations that determines the effective lifetime of minority charge carriers in macroporous silicon. The system of equations was found from the diffusion equation of minority carriers recorded for the macroporous layer and the single-crystal substrate. The solution of nonstationary diffusion equation written for a macroporous layer and a single-crystal substrate is complemented by boundary conditions at the surfaces of a sample of macroporous silicon and at the interface between the macroporous layer and the single-crystal substrate. The effective lifetime of minority charge carriers in macroporous silicon on a single crystal substrate depends on such values as: the minority carrier lifetime in the bulk, the diffusion coefficient of charge carriers, the thickness of the single crystal substrate, the average diameter of the macropores, the average distance between the centers of macropores, the surface recombination rate, the volume fraction macropore. The effective recombination of excess charge carriers in macroporous silicon is determined by the recombination of excess charge carriers on the surface of macropores and limited by the diffusion of charge carriers from the single crystal substrate to the recombination surfaces in the macroporous layer. Using the system of equations, we calculated and shown in the figure the effective lifetime of minority charge carriers in macroporous silicon dependent on the depth of the macropores. To verify the accuracy of calculations performed using a system of analytical equations, which determines the effective lifetime of minority charge carriers in macroporous silicon on a single crystal substrate, we used a numerical method. The numerical method showed the coincidence of the calculations on the effective lifetime of minority carriers. When the depth of macropores is close to the size of the sample of macroporous silicon, a discrepancy of calculations is observed.

Light-Tuned DC Conductance of Anatase TiO₂ Nanotubular Arrays: Features of Long-Range Charge Transport.

Experimental results related to the photoactivated dc conductance of anatase TiO2 nanotubular arrays (aTNTAs) under pulsed irradiation by a laser light inside and outside the fundamental absorption band are presented. It is found that the mobility and diffusion coefficients of charge carriers in the examined aTNTA are extremely low due to a strong charge-phonon coupling, abundance of shallow traps, and hopping conductivity between adjacent nanotubes. We consider that the confining electric field appeared within the array structure due to the difference in the local concentrations of excess electrons and holes at large values of the dc conductance suppresses the drift current. In this case, the dc conductance of such aTNTAs is mainly matured by the diffusion of mobile carriers. A recurrent kinetic model for evolution of the dc conductance of aTNTAs under laser irradiation has been proposed to interpret the experimental results.

Solid Biopolymer Electrolytes Based Carboxymethyl Cellulose Doped with Ammonium Fluoride: Ionic Transport and Conduction Mechanism

A series of solid biopolymer electrolytes (SBEs) based carboxymethyl cellulose doped with different weight percentage of ammonium fluoride, NH4F were prepared by the solution cast technique. The ionic conductivity was investigated using electrical impedance spectroscopy in the frequency range of 5 0Hz – 1 MHz. The highest ionic conductivity of 2.68 × 10−7 Scm−1 (9 wt.% NH4F) was obtained at ambient temperature. The ionic mobility and diffusion coefficient of charge carriers were identified to influence the enhancement of ionic conductivity in SBE samples. The exponent s of SBE samples were determined using Joncher's Universal Power Law. The conduction mechanism of the most conductive SBE sample can be represented by quantum mechanical tunnelling model.

Structure, equation of state and transport properties of molten calcium carbonate (CaCO3) by atomistic simulations

First-principle molecular dynamics (FPMD) calculations have been performed to evaluate the physical properties of liquid calcium carbonate (CaCO3), which are up to now poorly known. The liquid structure, the density, the atomic vibration motions, the diffusion coefficients of calcium and carbonate ions and the electrical conductivity have been evaluated. As compared with silicate melts, molten CaCO3 is characterized by a low density (∼2.25g/cm3 at 1623K and 0.5GPa), a viscosity almost as low as that of water (∼5mPas), and a high conductivity (∼200S/m). In using the FPMD calculations for benchmark, an empirical force field has been developed for predicting the properties of molten CaCO3 at any state point in the liquid stability field. This force field is implemented into a classical molecular dynamics (MD) code, much cheaper in computer time, and the equation of state and the phase diagram of the liquid phase have been obtained. The evolutions of the self diffusion coefficients, viscosity, and the electrical conductivity with pressure and temperature have been investigated and the results fitted with analytical forms. It is shown that the Stokes–Einstein equation, expressing the viscosity as a function of diffusion motion, is well followed, and that the Nernst–Einstein equation relating the electrical conductivity to the diffusion coefficients of charge carriers leads to an accurate prediction of the conductivity, provided that a constant correcting factor is applied. Consequently, viscosity and electrical conductivity of the liquid are found to be anticorrelated with each other and can be described by a simple law; λ=A/η0.9 (where A=1.905, λ is in S/m, and η in Pas).

Effect of anodic potential on process of formation of polyporphyrin film in solutions of tetrakis(p-aminophenyl)porphin in dichloromethane

The electrode impedance spectroscopy technique was used to study the process of formation of a conducting polyporphyrin film on a Pt electrode from a 10−3 M solution of tetrakis(p-aminophenyl)porphin in dichloromethane. An equivalent circuit is suggested for simulation of interface impedance in a wide range of working electrode potentials. It is shown that regions with a different mechanism of film formation are observed at an increase in potential from 0.0 to +1.0 V. The kinetics of film formation are studied at the potentials of +0.40, +0.60, and +0.80 V. It is found that good agreement is observed between the model and experimental data when the growing film is simulated using a Warburg element with a finite diffusion length. Conductivity and the diffusion coefficient of charge carriers in it are estimated on the basis of the suggested model for a film obtained at the potential of +0.40 V. It is shown that conductivity of a polyporphyrin film grows by more than an order of magnitude at an increase in deposition potential from +0.40 to +0.80 V.

All-Optical Technique to Correlate Defect Structure and Carrier Transport in Transferred Graphene Films

Chemical vapor deposition of graphene on copper foil is an attractive method of producing large-area graphene films, but the electronic performance is limited by defects such as creases from the film transfer process, wrinkles due to the thermal expansion coefficient mismatch, and grain boundaries from the growth process. Here we present an all-optical technique to correlate defect structure with electronic properties using spatially resolved Raman spectroscopy and transient absorption microscopy. This technique is especially attractive since it does not require any lithographic steps to probe the electronic properties of the graphene film. As a first demonstration, we focus on the effects of both wrinkles and creases while averaging over many small grains. It was found that wrinkles and creases may decrease the charge carrier diffusion coefficient by over 50% due to increased defect scattering. This technique may easily be extended to large grain graphene films in order to study the effect of different types of grain boundaries.

Ion conduction and space-charge polarization processes in Li2Ge7O15 crystals

The electrical properties of a lithium heptagermanate (Li2Ge7O15) crystal have been studied in DC and AC measuring fields at temperatures from 500 to 700 K. In a DC field, a substantial decrease of electrical conductivity σ with time has been detected. On the basis of kinetic dependences σ(t), estimates of the charge carrier diffusion coefficient D have been obtained. In the frequency range 101–105 Hz, the spectra of complex impedance ρ*(f) have been measured. The analysis of diagrams in the complex plane (ρ″–ρ′) has been performed within the equivalent circuit approach. It has been shown that, in the considered temperature and frequency intervals, the electrical properties of Li2Ge7O15 crystals have been determined by the hopping conduction of interstitial lithium ions A Li and accumulation of charge carriers near the blocking Pt electrodes.

Effect of electric field on diffusion in disordered materials. I. One-dimensional hopping transport

An exact analytical theory is developed for calculating the diffusion coefficient of charge carriers in strongly anisotropic disordered solids with one-dimensional hopping transport mode for any dependence of the hopping rates on space and energy. So far such a theory existed only for calculating the carrier mobility. The dependence of the diffusion coefficient on the electric field evidences a linear, non-analytic behavior at low fields for all considered models of disorder. The mobility, on the contrary, demonstrates a parabolic, analytic field dependence for a random-barrier model, being linear, non-analytic for a random energy model. For both models the Einstein relation between the diffusion coefficient and mobility is proven to be violated at any finite electric field. The question on whether these non-analytic field dependences of the transport coefficients and the concomitant violation of the Einstein's formula are due to the dimensionality of space or due to the considered models of disorder is resolved in the following paper [Nenashev et al., arXiv:0912.3169], where analytical calculations and computer simulations are carried out for two- and three-dimensional systems.

Measurements of the Einstein relation in doped and undoped molecular thin films

We present the Kelvin probe force microscopy measurements of the Einstein relation, i.e., the relation between the diffusion coefficient of charge carriers and their mobility, in undoped and doped disordered organic thin films. The theoretical prediction of a large deviation of the Einstein relation from its classical value is verified and attributed to the energy distribution of the density of states. The results are explained in the context of degeneracy effects on the transport in disordered organic thin films, and their implications for organic-based devices are discussed.

Redox polymer poly-N,N′-2,3-dimethylbutane-2,3-diyl-bis(salicylideniminato)nickel: An impedance spectroscopy study

Films of poly-N,N′-2,3-dimethylbutane-2,3-diyl-bis(salicylideniminato)nickel are studied by cyclic voltammetry and faradaic impedance methods in acetonitrile solutions containing 0.1 M tetraethylammonium tetrafluoroborate. The resistance to charge transfer and the double-layer capacitance, calculated from the semicircle in the high-frequency spectrum portion, are referred to the film/electrolyte interface. From the low- and mid-frequency impedance spectra portions, the low-frequency capacitance and the effective diffusion coefficient of charge carriers are determined. The assumption about a noticeable film porosity is shored up by direct scanning electron microscopy examination of film surfaces.

Coupled Electron‐Proton Transport in Electropolymerized Methylene Blue and the Influences of Its Protonation Level on the Rate of Electron Exchange with β‐Nicotinamide Adenine Dinucleotide

AbstractThis paper describes electrochemical characteristics of poly(methylene blue) electrolytically deposited on glassy carbon and examines the electrocatalytic activity of the polymer toward oxidation of the coenzyme NADH. Redox‐active properties of the cationic polyelectrolyte arose from both electron self‐exchange between electroactive sites and a high ionic film‐conductivity. The diffusion coefficient of charge carriers in the film increased with decreasing solution pH, indicating the pH dependence of the electron diffusion coefficient. The electrocatalytic oxidation of NADH at the polymer‐modified electrode proceeded via an intermediate charge‐transfer complex of the reduced polymer with the oxidized coenzyme. The complex dissociated more rapidly into the oxidation products as the reduced polymer protonated. Thus, the rate constant for the cross‐exchange reaction rose with a decrease in pH. For NADH oxidation, the polyelectrolyte exhibited an electrocatalytic activity higher than the monomeric dye because of a stronger oxidizing power of the second oxidized form of the polymer.

Scanning Probe Microscopy Studies of Solid-State Molecular Electroluminescent Devices Based on Tris(2,2‘-bipyridine) Ruthenium(II) Complexes

The charge injection, transport, and light emission of a solid-state molecular electrochemiluminescent thin (100 nm) film of tris(2,2‘-bipyridine) ruthenium(II) complex, Ru(bpy)3(ClO4)2, was investigated with tuning-fork-based scanning probe microscopy (TFSPM) in combination with electroluminescence and current measurements as a function of potential. Spin-cast [Ru(bpy)3(ClO4)2] thin films are shown to contain rather uniformly distributed nanostructures. These nanostructures produce heterogeneity in the current and luminescence responses of the films. Both single and double charge carrier (unipolar and bipolar) injection can take place in these thin films, depending on the magnitude of the bias voltage. Potential-step transients allow the determination of the effective diffusion coefficients of charge carriers. The effective diffusion coefficients of electrons or holes depend strongly on the electric field strength (or the applied voltage). We have also used the TFSPM to penetrate the [Ru(bpy)3(ClO4)2] th...

Deviation from the Einstein relation: mobility of unrelaxed carriers

The relation between the drift mobility and the diffusion coefficient of charge carriers in one-dimensional systems with energy disorder is investigated. By using the effective medium approximation, we derived expressions for these transport coefficients. The analytical results verified by computer simulations demonstrate that the Einstein relation is invalid during the energy relaxation of the charge carriers. Our findings suggest that under typical experimental conditions, the time-of-flight mobility of charge carriers is independent of the field strength and decreases with the sample thickness according to the power law.

Enhanced rate of the redox reaction of indigodisulfonate at electrodes coated with poly[1-methyl-3-(pyrrol-1-ylmethyl)pyridinium]chloride films

In order to answer the question of why poly[1-methyl-3-(pyrrol-1-ylmethyl)pyridinium]chloride films markedly increase the voltammetric current of indigodisulfonate (IS) ions, the authors have examined the impedance response of IS-loaded film electrodes at different oxidation levels and thicknesses of the loaded film. The standard heterogeneous rate constant at the modified electrodes is approximately three orders of magnitude lower than that at a bare electrode, because of the strong binding force of the redox anion to the polycationic film. Electron transport in the loaded film is appropriately described as a diffusion-like process due to intermolecular electron hopping. The diffusion coefficients of charge carriers suggest that electrons move much more slowly through the film than ions. In conclusion, the electrocatalytic effect produced by the polymer film is attributed to an effective extraction of IS from very dilute solutions (the partition coefficient is 2×10 5 ).

Dependence of redox-kinetic parameters at poly(o-phenylenediamine)-modified electrodes upon the oxidation and protonation levels of the polymer

Abstract The charge-transfer resistance, the redox capacitance and the diffusion coefficient of charge carriers at poly( o -phenylenediamine)-modified electrodes were determined by electrochemical impedance spectroscopy. Impedance results are interpreted in terms of the diffusion–migration transport of both electrons and protons through the film. Their coupled diffusion coefficients obtained at different potentials show a maximum near the formal potential of the polymer. This relationship between the oxidation level and the coupled diffusion coefficient indicates that the rate of charge transport within the film may be controlled by interchain electron-hopping. An exponential decrease in the coupled diffusion coefficient with increasing solution pH implies that the electron-hopping process is coupled with intermolecular proton exchange. Deprotonation of the polymer can result in a decrease in the homogeneous electron-transfer rate constant.

Anodic film growth on antimony in H 3PO 4 solutions

The anodic oxidation of Sb in H 3PO 4 solutions is studied within the frame of an investigation concerning the mechanism of the initial stages of anodic film growth on metals. In this special case, so-called induction periods of constant potential preceding the quasi-linear potential rise in a galvanostatic experiment are explained by a semiconductor layer formation on the Sb electrode. Proofs for this suggestion are furnished by determining the main electrochemical and electrophysical characteristics of the film, both during its growth and in steady-state conditions. These parameters include field strength, ionic conductivity, thickness, potential of zero photocurrent, photocurrent onset energy, dielectric constant and diffusion coefficient of charge carriers in steady-state conditions.