Diffusion-limited Process Research Articles

Oxygen plasma cleaning of copper for photocathode applications: A MEIS and XPS study

MEIS and XPS studies have been conducted for a range of oxygen plasma treated copper samples (and one treated with Ar plasma), as part of a study of the preparation of photocathode surfaces. This procedure was seen to remove hydrocarbon contamination, but left an oxide film whose thickness depended on the treatment conditions used. The film thickness was seen to increase with longer treatment time and higher RF power levels with behaviour characteristic of a diffusion limited process. Annealing led to a removal of the oxide layer by diffusion of oxygen into the bulk of the samples. This indicates that where the oxide layer is sufficiently thin, it should be possible to produce a surface with low enough oxygen content to have adequate conductivity and high enough surface escape probability to allow photoemission at UV wavelengths. Ar plasma treatment was seen to result in a very thin oxide film which could satisfy these requirements and thus might be preferable. Data from single crystal copper samples showed similar total oxygen content for all the surfaces analysed.

Diffusion Limited Escape Rate of a Complex Molecule in Multi-dimensional Confinement.

The rate at which a Brownian particle confined in a closed space escapes from the space by passing through a narrow passage is called the escape rate. The escape rate is relevant to many diffusion limited processes in polymer and colloidal systems, such as colloidal aggregation, polymerization reaction, polymer translocation through a membrane, etc. Here, we propose a variational principle to calculate the escape rate of complex molecules doing Brownian motion in a multi-dimensional phase space. We propose a regional minimization method in which we divide the whole phase space into regions, conduct the minimization for each region, and combine the results to get the minimum in the entire space. As an example, we discuss (1) the escape rate of a point particle that escapes from a confinement passing through a long corridor and (2) the escape rate of a rod-like particle that escapes through a small hole made in the wall of the confinement.

Deepening into the charge storage mechanisms and electrochemical performance of TiO2 hollandite for sodium-ion batteries

The electrochemical performance of TiO2 hollandite, TiO2(H), obtained by complete K+ ion extraction of the bronze K0.2TiO2 is investigated. TiO2 develops a fairly stable capacity of 106 mAh g–1 after 300 cycles at C/8 (42 mA g–1) and maintains 100 mAh g–1 after 600 cycles. At high current rate (2C, 671 mA g–1) 55 mAh g–1 is still maintained. Cycling produces nanosizing of the TiO2 electrode (to 200–300 nm) by electrochemical milling but cyclic voltammetry at different sweep rates indicates that diffusive controlled faradic contribution to the total capacity of TiO2(H) due to Na insertion is significant even at high current. However, participation of pseudocapacitive charge storage is unveiled. The voltage profile resembles in fact that of pseudocapacitive materials with no clear evidence of a constant voltage region. Operando XRD confirmed the lowering of symmetry from tetragonal I4/m to monoclinic I2/m upon sodiation with a relatively narrow two-phase region different from other long plateaus of typical battery materials. Cyclic voltammetry clearly indicates that the two peaks (centered at 1.25 and 0.5 V on reduction) correspond to diffusion-limited faradic processes. Thus, it can be said that hollandite TiO2 is a battery-like material, but for which kinetics is not limited by a biphasic transformation. Instead, kinetics is limited mainly by slow diffusion in single phases with variable composition (continuous variation of voltage vs. capacity) that are formed upon Na+ intercalation into the tunnels. The limited diffusion at high sweep rate favors the dominance of pseudocapacitance (charge transfer at the surface). A comparison with the bronze K0.2TiO2 reveals the importance of potassium in the electrochemical properties and the nature of the different physicochemical processes of both compounds.Sodium ion diffusion coefficient in TiO2(H), 2.6 · 10–13 cm2 s–1, is several orders of magnitude higher than that of TiO2 rutile and anatase, however it does not provide a fast intercalation into the tunnels to consider it a pseudocapacitive intercalation material.

(Invited) Extracting Kinetics from Scanning Electrochemical Microscopy Images through Least-Squares Fitting of Reactive Discs

The strength of scanning electrochemical microscopy measurements (SECM) is its ability to give insights into the kinetics of an underlying surface. Up to now there was no established way to extract kinetics from an SECM image. Our study fills this gap by proposing a method that fits the active area and kinetics of reactive sites from SECM images using the Levenberg-Marquardt algorithm and finite element method simulations.Currently, the kinetics of reactions at a surface are quantified through SECM by performing approach curves: measuring the SECM current as the microelectrode approaches a surface vertically.[1] The theory used to fit approach curves assumes that the kinetics at the surface are uniform across an infinitely large surface. Realistically, sites at which reactions occur in SECM imaging are not infinitely large, leading to an under-estimation of kinetics at finite reactive sites. In some cases, approach curve theory can misidentify diffusion-limited surface reactions at small sites as being electron-transfer-limited. Our new method instead assumes that reactive sites are uniformly reacting discs. High agreement between the fitted and true areas of reactive sites are shown for both simulated and experimental SECM images. Less than 10% error was common for nearly-circular reactive sites. Diffusion-limited processes are not mislabelled as electron-transfer-limited by this method. The rate constants for electron-transfer-limited reactions were usually fit to within 15% error, much lower than the error experienced by the approach-curve method when applied to finite reactive sites.[1] C. Lefrou, R. Cornut, Analytical Expressions for Quantitative Scanning Electrochemical Microscopy (SECM). ChemPhysChem 2010, 11, 547-556.

In-Situ Thermochemical Shock-Induced Stress at the Metal/Oxide Interface Enhances Reactivity of Aluminum Nanoparticles.

Although aluminum (Al) nanoparticles have been widely explored as fuels in energetic applications, researchers are still exploring approaches for tuning their energy release profile via microstructural alteration. In this study, we show that a nanocomposite (∼70 nm) of a metal ammine complex, such as tetraamine copper nitrate (Cu(NH3)4(NO3)2/TACN), coated Al nanoparticles containing only 10 wt. % TACN, demonstrates a ∼200 K lower reaction initiation temperature coupled with an order of magnitude enhancement in the reaction rate. Through time/temperature-resolved mass spectrometry and ignition onset measurements at high heating rates, we show that the ignition occurs due to a condensed phase reaction between Al and copper oxide (CuO) crystallized on TACN decomposition. TEM and XRD analyses on the nanoparticles at an intermediate stage show that the rapid heat release from TACN decomposition in-situ enhances the strain on the Al core with induction of nonuniformities in the thickness of its AlOx shell. The thinner region of the nonuniform shell enables rapid mass transfer of Al ions to the crystallized CuO, enabling their condensed phase ignition. Hence, the thermochemical shock from TACN coating induces stresses at the Al/AlOx interface, which effectively switches the usual gas phase O2 diffusion-limited ignition process of Al nanoparticles to become condensed phase Al ion transfer controlled, thereby enhancing their reactivity.

Degradation of Per- and Polyfluoroalkyl Substances with Hydrated Electrons: A New Mechanism from First-Principles Calculations.

Per- and polyfluoroalkyl substances (PFASs) are synthetic contaminants found in drinking groundwater sources and a wide variety of consumer products. Because of their adverse environmental and human health effects, remediation of these persistent compounds has attracted significant recent attention. To gain mechanistic insight into their remediation, we present the first ab initio study of PFAS degradation via hydrated electrons─a configuration that has not been correctly considered in previous computational studies up to this point. To capture these complex dynamical effects, we harness ab initio molecular dynamics (AIMD) simulations to probe the reactivities of perfluorooctanoic (PFOA) and perfluorooctane sulfonic acid (PFOS) with hydrated electrons in explicit water. We complement our AIMD calculations with advanced metadynamics sampling techniques to compute free energy profiles and detailed statistical analyses of PFOA/PFOS dynamics. Although our calculations show that the activation barrier for C-F bond dissociation in PFOS is three times larger than that in PFOA, all the computed free energy barriers are still relatively low, resulting in a diffusion-limited process. We discuss our results in the context of recent studies on PFAS degradation with hydrated electrons to give insight into the most efficient remediation strategies for these contaminants. Most importantly, we show that the degradation of PFASs with hydrated electrons is markedly different from that with excess electrons/charges, a common (but largely incomplete) approach used in several earlier computational studies.

Determining the depth of surface charging layer of single Prussian blue nanoparticles with pseudocapacitive behaviors

Understanding the hybrid charge-storage mechanisms of pseudocapacitive nanomaterials holds promising keys to further improve the performance of energy storage devices. Based on the dependence of the light scattering intensity of single Prussian blue nanoparticles (PBNPs) on their oxidation state during sinusoidal potential modulation at varying frequencies, we present an electro-optical microscopic imaging approach to optically acquire the Faradaic electrochemical impedance spectroscopy (oEIS) of single PBNPs. Here we reveal typical pseudocapacitive behavior with hybrid charge-storage mechanisms depending on the modulation frequency. In the low-frequency range, the optical amplitude is inversely proportional to the square root of the frequency (∆I ∝ f−0.5; diffusion-limited process), while in the high-frequency range, it is inversely proportional to the frequency (∆I ∝ f−1; surface charging process). Because the geometry of single cuboid-shaped PBNPs can be precisely determined by scanning electron microscopy and atomic force microscopy, oEIS of single PBNPs allows the determination of the depth of the surface charging layer, revealing it to be ~2 unit cells regardless of the nanoparticle size.

Sessile droplet evaporation in the atmosphere of different gases under forced convection

The phenomenon of evaporation from the surface of a liquid droplet into a neutral noncondensible gas was numerically studied by taking forced convection gaseous flow into account. The mathematical model considers the effects of surface tension, gravitational force, viscosity of both liquid and gaseous media, as well as the Stefan flow from the droplet surface, possible free gravitational convection, and the Marangoni convection in droplets, and it is designed to describe diffusion-limited evaporation. We consider the diffusion-limited evaporation process when the diffusive gas flux to the droplet surface is compensated by the convective Stefan flow from the surface. The results indicate an interaction of the liquid and gaseous media. Convective gas flows cause the liquid to move and a vortex to occur in the droplet. The flow velocities in a vortex are 103 times less than the characteristic velocity of forced convection flow in air. The droplet surrounded by gaseous flow changes its shape and oscillates, which causes a gas-density wave. Calculations have shown that the diffusion-limited evaporation rate does not change in the presence of forced convection, which contradicts most of the known experimental works. The possible reason for this discrepancy is the presence of non-equilibrium conditions at the liquid–gas interface in experiments. This leads to a consequent change of the evaporation mode to non-diffusive, while the numerical model postulates the Stefan condition and diffusion-limited evaporation.

Homogeneous Optical Line Widths in Hybrid Ruddlesden–Popper Metal Halides Can Only Be Measured Using Nonlinear Spectroscopy

The homogeneous photoluminescence spectral linewidth in semiconductors carries a wealth of information on the coupling of primary photoexcitations with their dynamic environment as well as between multi-particles. In the limit in which inhomogeneous broadening dominates the total optical linewidths, the inhomogeneous and homogeneous contributions can be rigorously separated by temperature-dependent %linear spectral measurements such as steady-state photoluminescence spectroscopy. This is possible because the only temperature-dependent phenomenon is optical dephasing, which defines the homogeneous linewidth, since this process is mediated by scattering with phonons. However, if the homogeneous and inhomogeneous linewidths are comparable, as is the case in hybrid Ruddlesden-Popper metal halides, the temperature dependence of linear spectral measurement \emph{cannot} separate rigorously the homogeneous and inhomogeneous contributions to the total linewidth because the lineshape does \emph{not} contain purely Lorentzian components that can be isolated by varying the temperature. Furthermore, the inhomogeneous contribution to the steady-state photoluminescence lineshape is not necessarily temperature independent if driven by diffusion-limited processes, particularly if measured by photoluminescence. Nonlinear coherent optical spectroscopies, on the other hand, do permit separation of homogeneous and inhomogeneous line broadening contributions in all regimes of inhomogeneity. Consequently, these offer insights into the nature of many-body interactions that are entirely inaccessible to temperature-dependent linear spectroscopies. When applied to Ruddlesden-Popper metal halides, these techniques have indeed enabled us to quantitatively assess the exciton-phonon and exciton-exciton scattering mechanisms.

Sodium tungsten oxide nanowires-based all-solid-state flexible transparent supercapacitors with solar thermal enhanced performance

A sodium tungsten oxide (NaxWO3) nanowires-based all-solid-state flexible transparent supercapacitor with solar thermal enhanced performance has been developed owing to the good visible light transparency and near infrared (NIR) photothermal conversion property of NaxWO3. Firstly, silver nanowires (AgNWs) and NaxWO3 nanowires were synthesized by polyol and hydrothermal methods, respectively. Secondly, AgNWs, NaxWO3 nanowires and poly(3,4-ethylenedioxythiophene):polystyrene sulfonate (PEDOT:PSS) were coated on polyethylene terephthalate (PET) film in sequence to yield the AgNWs/NaxWO3/PEDOT electrode, which was shown to exhibit good capacitive property in H2SO4 solution. Finally, the PEDOT//AgNWs/NaxWO3/PEDOT all-solid-state flexible transparent asymmetric supercapacitor was fabricated by using this electrode as the negative electrode, PEDOT:PSS-coated PET film as the positive electrode, and poly(acrylic acid)/sulfuric acid (PAA/H2SO4) gel as the electrolyte. It possessed good visible light transparency, flexibility, and capacitive property. Furthermore, its capacitance could be significantly enhanced by solar illumination because the generated heat via NIR photothermal conversion of NaxWO3 nanowires could raise the temperature and thereby lower the electrolyte and charge-transfer resistances effectively. The further kinetic analysis confirmed that its solar thermal-enhanced capacitance was mainly contributed by the diffusion-limited process. Moreover, it exhibited good stability and both its energy density and power density could be enhanced by solar illumination. Such a novel supercapacitor might have great potential in the development of flexible transparent energy storage devices with solar thermal enhanced performance.

Charge dynamics in CuInS2 photovoltaic devices with In2S3 as buffer layer

The charge carrier dynamics of photovoltaic devices composed of FTO/TiO2/In2S3/CuInS2/graphite (FTO=Fluorine doped Tin Oxide) is investigated by Intensity Modulated Photocurrent Spectroscopy (IMPS) and Intensity Modulated Photovoltage Spectroscopy (IMVS). Characteristic lifetimes and transport times are obtained. The dependence of the lifetime with light intensity can be explained by multitrapping processes, which justify the rather long lifetimes. Moreover, typical spectral features in the Nyquist plots are obtained by a model based on the continuity equation where diffusion is the major transport process, as confirmed by the dependence of the transport times on the externally applied potential. Changes from a kinetically limited process to a diffusion limited process are observed by modifying the excitation wavelength. Moreover, the existence of a potential barrier or a similar limitation process at the In2S3/CuInS2 interface could be inferred by comparing of the experimental IMPS measurements with data derived from. The existence of defect states at the In2S3 can be deduced from the IMVS dependence with wavelength. Also, different capacitive effects in the samples can be discriminated due to the spectroscopic nature of the techniques here employed.

Mesoporous Zeolitic Imidazolate Frameworks

The zeolitic imidazolate frameworks (ZIFs) with three-dimensional periodic micropores encounter the barrier of the mass transfer in the diffusion-limited processes. To solve this question, the zeol...

Electrochemical impedimetric analysis of different dimensional (0D–2D) carbon nanomaterials for effective biosensing of L-tyrosine

Electrochemical biosensors employing nano-transduction surfaces are considered highly sensitive to the morphology of nanomaterials. Various interfacial parameters namely charge transfer resistance, double layer capacitance, heterogeneous electron transfer rate and diffusion limited processes, depend strongly on the nanostructure geometry which eventually affects the biosensor performance. The present work deals with a comparative study of electrochemical impedance-based detection of L-tyrosine (or simply tyrosine) by employing carbon nanostructures (graphene quantum dots, single walled carbon nanotubes (CNTs) and graphene) along with tyrosinase as the bio-receptor. Specifically, the role of carbon nanostructures (i.e. 0D, 1D and 2D) on charge transfer resistance is investigated by applying time-varying electric field at the nano-bioelectrode followed by calculating the heterogeneous electron transfer rate, double layer capacitor current and their effects on limits of detection and sensitivities towards tyrosine recognition. A theoretical model based on Randel’s equivalent circuit is proposed to account for the redox kinetics at various carbon nanostructure/enzyme hybrid surfaces. It was observed that, the 1D morphology (single walled CNTs) exhibited lowest charge transfer resistance ∼2.62 kΩ (lowest detection limit of 0.61 nM) and highest electron transfer rate ∼0.35 μm s−1 (highest sensitivity 0.37 kΩ nM−1 mm−2). Our results suggest that a suitable morphology of carbon nanostructure would be essential for efficient and sensitive detection of tyrosine.

Impedance scaling for gold and platinum microelectrodes

Objective. Electrical measurement of the activity of individual neurons is a primary goal for many invasive neural electrodes. Making these ‘single unit’ measurements requires that we fabricate electrodes small enough so that only a few neurons contribute to the signal, but not so small that the impedance of the electrode creates overwhelming noise or signal attenuation. Thus, neuroelectrode design often must strike a balance between electrode size and electrode impedance, where the impedance is often assumed to scale linearly with electrode area. Approach and main results. Here we study how impedance scales with neural electrode area and find that the 1 kHz impedance of Pt electrodes (but not Au electrodes) transitions from scaling with area (r −2) to scaling with perimeter (r −1) when the electrode radius falls below 10 µm. This effect can be explained by the transition from planar to spherical diffusion behavior previously reported for electrochemical microelectrodes. Significance. These results provide important intuition for designing small, single unit recording electrodes. Specifically, for materials where the impedance is dominated by a pseudo-capacitance that is associated with a diffusion limited process, the total impedance will scale with perimeter rather than area when the electrode size becomes comparable with the diffusion layer thickness. For Pt electrodes this transition occurs around 10 µm radius electrodes. At even lower frequencies (1 Hz) impedance approaches a constant. This transition to r −1 scaling implies that electrodes with a pseudo-capacitance can be made smaller than one might expect before thermal noise or voltage division limits the ability to acquire high-quality single-unit recordings.

Dynamic Plasticity Model for Rapidly Heated 1045 Steel Up to 1000 °C.

The National Institute of Standards and Technology (NIST) developed an experimental technique to measure the dynamic flow stress of metals under rapid heating to study their time-dependent plastic response when heating times are short enough to interrupt or bypass thermally driven microstructural evolution. Such conditions may exist as chips are formed in the machining process. Measurements of American Iron and Steel Institute1045 steel behavior up to 1000 °C showed complex thermal softening due to dynamic strain aging effects and the diffusion-limited austenite transformation process beginning at the A1 temperature (712 °C). This paper proposes a constitutive model to capture the flow stress and hardening evolution of 1045 steel under rapidly heated conditions for simulating metal cutting. The model combines the Preston-TonksWallace plasticity model, which uses five parameters to capture complex rate- and temperature-sensitive strain hardening, with a dual-ratesensitivity model to capture the response of rapidly heated 1045 steel. Finally, a strain-rate-dependent Gaussian function is introduced to capture dynamic strain aging effects, which act over a narrow range of temperatures that change with strain rate. The proposed model is compared to existing plasticity models for 1045 steel over the range of data available and at a representative machining condition.

Oxidation Behavior of InAlN during Rapid Thermal Annealing

Leakage currents in InAlN/GaN‐based high‐electron‐mobility transistors considered for normally‐off devices critically depend on the oxidation behavior of InAlN thin films. Herein, lattice‐matched InAlN thin films deposited on GaN (0001) are rapid thermally annealed at 800 °C in an oxygen‐rich environment. Aberration‐corrected scanning transmission electron microscopy combined with electron energy‐loss spectroscopy is used to systematically characterize the oxidation behavior of InAlN films as a function of annealing time. Initial growth of oxide layers is found to be reaction limited, which is replaced by a diffusion limited growth process once a critical thickness of the oxide layer is obtained. Growing oxide layers are amorphous and become porous with increasing annealing time.

Stationary distribution convergence of the offered waiting processes in heavy traffic under general patience time scaling

We study a sequence of single server queues with customer abandonment (\(GI/GI/1+GI\)) under heavy traffic. The patience time distributions vary with the sequence, which allows for a wider scope of applications. It is known Lee and Weerasinghe (Stochastic Process Appl 121(11):2507–2552, 2011) and Reed and Ward (Math Oper Res 33(3):606–644, 2008) that the sequence of scaled offered waiting time processes converges weakly to a reflecting diffusion process with nonlinear drift, as the traffic intensity approaches one. In this paper, we further show that the sequence of stationary distributions and moments of the offered waiting times, with diffusion scaling, converge to those of the limit diffusion process. This justifies the stationary performance of the diffusion limit as a valid approximation for the stationary performance of the \(GI/GI/1+GI\) queue. Consequently, we also derive the approximation for the abandonment probability for the \(GI/GI/1+GI\) queue in the stationary state.

Deeper Insights into the Bohart-Adams Model in a Fixed-Bed Column.

The Bohart-Adams model was one of the most widely used breakthrough models in column experiments. However, it usually provided a poor fit for the modeling of an asymmetric breakthrough curve. This work proposed the n-order Bohart-Adams and fractal-like Bohart-Adams models. The former indicated a nonlinear decay process of the concentration of the adsorbate or residual capacity of the adsorbent, while the latter reflected a diffusion-limited process on the heterogeneous surfaces. The Bohart-Adams and modified Bohart-Adams models were mathematically equivalent. The applicability of the n-order Bohart-Adams and fractal-like Bohart-Adams models was validated by norfloxacin and Cu(II) adsorption in a fixed-bed column. Compared with the Bohart-Adams model, the two new models had better fitting performance with higher R2 and lower χ2 values, and all of the residuals were randomly distributed. The fractal-like Bohart-Adams and modified dose-response models provided the best fitting quality for the adsorption of Cu(II) (R2 = 0.9956 and χ2 = 7.56 × 10-4) and norfloxacin (R2 = 0.9991 and χ2 = 1.37 × 10-4), respectively. This work may provide a practical method for the modeling of the asymmetric breakthrough curves.

Cover Feature: Oxygen Nucleation of MoS2 Nanosheet Thin Film Supercapacitor Electrodes for Enhanced Electrochemical Energy Storage (ChemSusChem 14/2021)

The Cover Feature shows that electrochemical exfoliation and oxygen nucleation of MoS2 nanosheet thin film supercapacitor electrodes results in enhanced capacitance. The nucleation and growth of the MoS2−xOx phase also shifts the charge storage process of the MoS2 nanosheet thin film supercapacitors from a diffusion-limited process to a capacitive-dominant process. More information can be found in the Full Paper by S. N. Lou et al.

Oxygen Nucleation of MoS2 Nanosheet Thin Film Supercapacitor Electrodes for Enhanced Electrochemical Energy Storage.

A direct thin film approach to fabricate large-surface MoS2 nanosheet thin film supercapacitors using the solution-based diffusion of thiourea into an anodized MoO3 thin film was investigated. A dense MoS2 nanosheet thin film electrode (D-MoS2 ) was obtained when the anodized MoO3 thin film was processed in a low thiourea solution concentration, whereas a highly porous MoS2 nanosheet thin film electrode (P-MoS2 ) was formed at a higher thiourea solution concentration. The charge storage performances of the D-MoS2 and P-MoS2 thin films displayed an unusual increase in capacitance on extended cycling, leading to a capacitance as high as around 5-8 mF cm-2 . X-ray diffraction and cross-sectional microscopy revealed the capacitance enhancements of the MoS2 supercapacitors are attributable to the nucleation of a new MoS2-x Ox phase upon cycling. For the D-MoS2 nanosheet thin film, the formation and growth of the MoS2-x Ox phase during cycling was accompanied by a volumetric expansion of the MoS2 layer. For the P-MoS2 thin film, the nucleation and growth of the MoS2-x Ox phase occurred in the pores of the MoS2 layer. The propagation of the MoS2-x Ox phase also shifted the charge storage process in both films from a diffusion-limited process to a capacitive-dominant process.