Diffusion-limited Process Research Articles

Transient Simulation of Diffusion-Limited Electrodeposition Using Volume of Fluid (VOF) Method

A numerical model utilizing the volume of fluid (VOF) method is proposed to simulate the transient shape changes of the deposit front, considering the diffusion-limited electrodeposition process. Modeling equations are proposed to accurately handle transport phenomena in both electrolyte (fluid) and deposit (solid). Transient evolutions of field structures, including flow, concentration, electric current density, and electric potential, are computed considering electrodeposited copper bumps. Two cases, including single cavity and multiple cavities, are studied. Based on the modeling results, the maximum height of the hump and the thickness of the deposited layer in each consecutive cavity decreases going from upstream to downstream. Conversely, the location of the maximum height of the hump remains unchanged in all cavities. Results are validated against available experiments.

Exciton annihilation in molecular aggregates suppressed through quantum interference.

Exciton-exciton annihilation (EEA), an important loss channel in optoelectronic devices and photosynthetic complexes, has conventionally been assumed to be an incoherent, diffusion-limited process. Here we challenge this assumption by experimentally demonstrating the ability to control EEA in molecular aggregates using the quantum phase relationships of excitons. We employed time-resolved photoluminescence microscopy to independently determine exciton diffusion constants and annihilation rates in two substituted perylene diimide aggregates featuring contrasting excitonic phase envelopes. Low-temperature EEA rates were found to differ by more than two orders of magnitude for the two compounds, despite comparable diffusion constants. Simulated rates based on a microscopic theory, in excellent agreement with experiments, rationalize this EEA behaviour based on quantum interference arising from the presence or absence of spatial phase oscillations of delocalized excitons. These results offer an approach for designing molecular materials using quantum interference where low annihilation can coexist with high exciton concentrations and mobilities.

A numerical solution on pore diffusion equation with a volume of limited bath boundary condition using the finite difference method

Abstract Numerical approaches have long been used to examine material behaviors that are governed by diffusion. The surface water and groundwater become polluted with regard to time. The pollutants travel from place to place in extended time intervals interacting with the solid soil particles. The diffusion of solute with solid soil particles idealized as spheres are studied in this dissertation. The objective was to numerically simulate diffusion through a sphere. A steady-state finite difference method was used to study the diffusion in a sphere. It was assumed that a bulk liquid solution interacts with solid spheres through a diffusion limited process which is equivalent to a volume of limited bath boundary condition. A sphere of radius 0.07 cm is placed in the beaker containing the solution. The radius of the sphere is divided into 15 nodes each of radius 0.005 cm. Initially, the sphere is free from the solute. As time progresses the diffusion in the sphere takes place. The solute from outside the sphere gets infused in the sphere. By using a numerical technique, the concentration at different nodes at different time intervals is studied. The process is carried out for two different solutions with different concentration values.

Electrocatalytic oxygen reduction reaction at FeS2-CNT/GCE surface in alkaline medium

The oxygen reduction reaction (ORR) has attracted more attention in recent time due to its wide applications in electrochemical energy transformation such as fuel cells, metal-air batteries, electrolyzers, and wastewater treatment. However, the development of inexpensive and highly efficient ORR electrocatalysts is still a great challenge. Herein, FeS2-carbon nanotube (CNT) nanocomposite was fabricated and deposited on a glassy carbon electrode (GCE) surface to inspect the electrocatalytic ORR in an alkaline medium. Scanning electron microscopy (SEM), transmission electron microscopy (TEM), energy dispersive X-ray spectroscopy (EDX), X-ray photoelectron spectroscopy (XPS), and X-ray diffraction (XRD) were utilized to characterize the FeS2-CNT/GCE surface. The EIS and open circuit potential (OCP) analysis showed that the FeS2-CNT/GCE has excellent catalytic effects compared to a bare GCE. Kinetic investigations revealed that the ORR occurred through a consecutive reaction pathway accompanied by a fast electron transfer step and controlled by a diffusion-limited process. Analysis of hydrodynamic voltammograms confirmed that the oxygen molecules undergo a 2e- transfer irreversible redox process and HO2- is generated as an intermediate before converting into hydroxide as the final product. The standard rate constant was calculated to be 2.5 × 10−7 cms−1 and the reaction followed first order kinetics.

Co-electrodeposited poly (3, 4-ethylenedioxythiophene) (PEDOT)-multiwall carbon nanotubes (MWCNT) hybrid electrodes based solid-state supercapacitors using ionic liquid gel electrolyte for energy storage with pulsed power capabilities

Electrochemical and energy storage properties of poly(styrene sulfonate) doped poly (3, 4-ethylenedioxythiophene) (PEDOT:PSS) conducting polymer hybridized with the multiwall carbon nanotubes (MWCNT) are studied as solid-state supercapacitor with anion-doped ionic liquid (IL) gel electrolyte. The PEDOT: PSS-MWCNT composite electrodes were formed by co-electrodeposition using sequential 4 mA cm−2 current density with 10 ms current pulses in an aqueous medium with highly dispersed MWCNTs using Na-dodecyl sulfate (SDS) surfactant, PSS dopant (10–20 %) and EDOT monomer. Raman spectral study confirms with ≤10%PSS, the MWCNTs are moored into PEDOT chains via covalent bonding with carbons at α and β-position as PEDOT grows over flexible graphite substrate. Specific capacitance of 138 F g−1 discerned from cyclic voltammetry in IL-gel electrolyte is higher than reported in liquid electrolytes and chemically polymerized electrodes. Electrical double layer (EDL) capacitance analysis shows high 71.2 mF cm−2 contribution originated from MWCNTs with 10 % PSS, and slightly lower 48.8 mF cm−2 with 20 % PSS. The performance optimized PEDOT: PSS (10 %)- MWCNT (1 mg) based supercapacitors show large (43 %) access to the electroactive nanoporous surface regions contributing to capacitive charge and 57 % electrode has access to charge storage via diffusion limited Faradaic process. Nyquist plots analyzed for Warburg coefficient show minimal charge transfer resistance unimpacted by ionic diffusion. From the frequency response of the real and imaginary impedances pulsed power is assessed as 6.33 kW kg−1 at energy density 3.43 Wh kg−1. Charge-discharge behavior of optimized supercapacitor over 0.05–2.0 A g−1 current densities is triangular, highly symmetrical. Ragone plot shows high energy density of 7.7 Wh kg−1 at specific power 5.3 kW kg−1 plateauing out to 4.4 Wh kg−1 at higher specific power of 11.5 kW kg−1. Charge-discharge cycle analysis shows merely 20 % loss of specific capacitance by ∼500 cycles largely stabilizing for over 2000 cycles while the Coulomb efficiency remaining invariant at 95 %.

Sculpting In-plane Fractal Porous Patterns in Two-Dimensional MOF Nanocrystals for Photoelectrocatalytic CO2 Reduction.

Herein, by choosing few-nm-thin two-dimensional (2D) nanocrystals of MOF-5 containing in-planner square lattices as a modular platform, a crystal lattice-guided wet-chemical etching has been rationally accomplished. As a result, two attractive pore patterns carrying Euclidean curvatures; precisely, plus(+)-shaped and fractal-patterned pores via ⟨100⟩ and ⟨110⟩ directional etching, respectively, are regulated in contrast to habitually formed spherical-shaped random etches on MOF surface. In agreement with the theoretical calculations, a diffusion-limited etching process has been optimized to devise high-yield of size-tunable fractal-pores on the MOF surface that tenders for a compatibly high payload of catalytic ReI -complexes using the existing large edge area once modified into a free amine-group-exposed inner pore surface. Finally, on benefiting from the long-range fractal opening in 2D MOF support structure, while loaded on an electrode surface, a facilitated cross-interface charge-transportation and well-exposure of immobilized ReI -catalysts are anticipated, thus realizing enhanced activity and stability of the supported catalyst in photoelectrochemical CO2 -to-CO reduction.

Relationship between Rate-Limiting Process and Scaling Law in Gel Growth Induced by Liquid-Liquid Contact.

Gelation through the liquid-liquid contact between a polymer solution and a gelator solution has been attempted with various combinations of gelator and polymer solutions. In many combinations, the gel growth dynamics is expressed as X∼t, where X is the gel thickness and t is the elapsed time, and the scaling law holds for the relationship between X and t. In the blood plasma gelation, however, the crossover of the growth behavior from X∼t in the early stage to X∼t in the late stage was observed. It was found that the crossover behavior is caused by a change in the rate-limiting process of growth from the free-energy-limited process to the diffusion-limited process. How, then, would the crossover phenomenon be described in terms of the scaling law? We found that the scaling law does not hold in the early stage owing to the characteristic length attributable to the free energy difference between the sol-gel phases, but it does in the late stage. We also discussed the analysis method for the crossover in terms of the scaling law.

Transient Polarization and Dendrite Initiation Dynamics in Ceramic Electrolytes

Solid-state electrolytes, by enabling lithium metal anodes, may significantly increase the energy density of current lithium-ion batteries. However, similar to their liquid counterparts, these hard and stiff electrolytes can still be penetrated by soft Li metal, above a critical current density (CCD). The prevailing method to determine the CCD employs step-wise galvanostatic cycling, which suffers from inconsistent active interfacial areas due to void formations after repeated stripping and plating, leaving large variance in the reported data that preclude precision understandings. Here, we combine a one-way polarization technique with electrochemical impedance spectroscopy to uncover, for the first time, the existence of significant polarization dynamics in ceramic electrolytes. In contrast to the diverging transient current due to metal penetration, the current peaks we observed suggest a diffusion-limited mechanism that follows the classic Randles-Sevcik equation for analyzing the diffusion-limited processes in liquid electrolytes. Our results allow a rigorous self-consistent analysis to reveal that the CCD is a diffusion-limited current density, while the system-specific limiting current density for ceramic electrolytes is still lower than CCD, which suggests that the ion transport mechanism preceding the dendrite penetration in ceramic electrolytes is unifiable with that in liquid electrolytes.

Comparison of interfacial reactions and isothermal aging of cone Ni-P and flat Ni-P with Sn3.5Ag solders

Electroless Ni-P plating has good prospects for application as a diffusion barrier layer for interfacial reactions. In this study, the interfacial reaction between the microcone-structured Ni-3.5%P coating with high crystallinity and the Sn3.5Ag solder was investigated and compared with Sn3.5Ag/flat-Ni-(2%, 5%, 10%)P couples. Wettability experiments of Sn3.5Ag on four types of Ni-P coatings were carried out. Reflow at 250 °C for various minutes was performed, as well as isothermal aging experiments at 175 °C for various durations. The results showed that the Sn3.5Ag achieved the best wettability on cone Ni-3.5%P due to the pyramidal morphology that provides an additional driving force for wetting. During isothermal aging, the growth of intermetallics (IMCs) in the Sn3.5Ag/cone-Ni-3.5%P couple was attributed to the contribution of boundary diffusion mechanism to the rate control process, while that in the remaining three couples was a grain boundary diffusion-limited process. After reflow and isothermal aging, fewer microvoids and no harmful Ni-Sn-P layers were detected in the interface of Sn3.5Ag/cone-Ni-3.5%P couples, while they were detected in the other three couples, indicating that the cone Ni-3.5%P couple could inhibit the formation of Ni-Sn-P layer and microvoids. As a result, Sn3.5Ag/cone Ni-3.5% couples exhibited better shear resistance.

Diffusion controlled early-stage L12-D023 transitions within Al3Zr

Antiphase boundary (APB) in Al3Zr was regarded to play an important role in the L12-D023 phase transition, the formation of which has long been explained through the shearing/slipping mechanism. Herein, the detailed atomic structures of conservative {100} APBs within L12-Al3Zr particles forming at the early-stage of L12-D023 transition in an Al-Zr alloy were systematically studied by high angle annual dark-field scanning transmission electron microscope (HAADF-STEM). As a strong evidence of diffusion-limited phase transformation process, significant de-ordering of atoms in APBs and the neighboring atomic planes have been found. By analyzing the two possible pathways, it is suggested that L12-D023 phase transition has been achieved through a diffusion mechanism, instead of shearing mechanism while the formation of APB is an intermediate stage of the phase transition process. First principles density functional theory (DFT) reveals that the formation of APBs and subsequent phase transition are energetically favorable, which provide the driving force for diffusion.

Geochemistry and Geometrical Features of the Upper Cretaceous Vitulano Para-Autochthonous Karst Bauxites (Campania Region, Southern Italy): Constraints on Genesis and Deposition

In the Vitulano area, Upper Cretaceous bauxite bodies fill small depressions and karst cavities within Cretaceous shallow-water limestones. These bauxites were studied to understand the processes that led to their formation. Geochemical, mineralogical, and petrographic analyses were carried out on the bauxite samples, together with image analysis providing geometric parameters. The texture of Vitulano bauxite consists of ooids and sub-circular aggregates dispersed in a predominantly Ca-rich matrix. Ooids are generally formed by a single large core, often surrounded by an alternation of different aggregates of boehmite and Al-hematite reflecting different climate periods. The composition is dominated by the major elements Al2O3 and CaO with lower concentrations of Fe2O3 and SiO2. Boehmite, calcite, hematite, and anatase are the main mineralogical phases identified. Image analysis provided values of fractal dimension D that gives information on carbonate platform exposure times since it is linked to long-lasting sub-aerial events and diffusion-limited cluster aggregation processes. The tectonic evolution of the area played an important role in the genesis of the Vitulano bauxites since it favored the erosion, transport, and re-deposition of pre-existing bauxite material from the surrounding Campania bauxites. Based on this hypothesis, Vitulano bauxites are defined and classified as para-autochthonous, and this was supported by Eu/Eu* vs. Sm/Nd and Eu/Eu* vs. TiO2 Al2O3 indices displaying a similarity between Vitulano and the other Campania bauxites.

Mineral Nanoparticle Aggregation Alters Contaminant Transport under Flow.

Iron oxyhydroxide nanoparticle reactivity has been widely investigated, yet little is still known on how particle aggregation controls the mobility and transport of environmental compounds. Here, we examine how aggregates of goethite (α-FeOOH) nanoparticle deposited on 100-300 μm quartz particles (GagCS) alter the transport of two emerging contaminants and two naturally occurring inorganic ligands-silicates and phosphates. Bromide tracer experiments showed no water fractionation into mobile and immobile water zones in an individual goethite-coated sand (GCS) column, whereas around 10% of the total water was immobile in a GagCS column. Reactive compounds were, in contrast, considerably more mobile and affected by diffusion-limited processes. A new simulation approach coupling the mobile-immobile equation with surface complexation reactions to surface reactive sites suggests that ∼90% of the binding sites were likely within the intra-aggregate zones, and that the mass transfer between mobile and immobile fractions was the rate-limited step. The diffusion-controlled processes also affected synergetic and competitive binding, which have otherwise been observed for organic and inorganic compounds at goethite surfaces. These results thereby call for more attention on transport studies, where tracer or conservative tests are often used to describe the reactive transport of environmentally relevant molecules.

Surface-redox sodium-ion storage in anatase titanium oxide

Sodium-ion storage technologies are promising candidates for large-scale grid systems due to the abundance and low cost of sodium. However, compared to well-understood lithium-ion storage mechanisms, sodium-ion storage remains relatively unexplored. Herein, we systematically determine the sodium-ion storage properties of anatase titanium dioxide (TiO2(A)). During the initial sodiation process, a thin surface layer (~3 to 5 nm) of crystalline TiO2(A) becomes amorphous but still undergoes Ti4+/Ti3+ redox reactions. A model explaining the role of the amorphous layer and the dependence of the specific capacity on the size of TiO2(A) nanoparticles is proposed. Amorphous nanoparticles of ~10 nm seem to be optimum in terms of achieving high specific capacity, on the order of 200 mAh g−1, at high charge/discharge rates. Kinetic studies of TiO2(A) nanoparticles indicate that sodium-ion storage is due to a surface-redox mechanism that is not dependent on nanoparticle size in contrast to the lithiation of TiO2(A) which is a diffusion-limited intercalation process. The surface-redox properties of TiO2(A) result in excellent rate capability, cycling stability and low overpotentials. Moreover, tailoring the surface-redox mechanism enables thick electrodes of TiO2(A) to retain high rate properties, and represents a promising direction for high-power sodium-ion storage.

Highly efficient and stable hydrodechlorination of chlorophenols in a flow Pd–Ce/SiO2/Ni foam reactor

The foam reactor shows attractive potential for employment in fast and often diffusion limited processes such as hydrodechlorination (HDC).

Interpreting inorganic compositional depth profiles to understand the rate-limiting step in vapor phase infiltration processes.

Vapor phase infiltration (VPI) is a post-polymerization modification technique that infuses inorganics into polymers to create organic-inorganic hybrid materials with new properties. Much is yet to be understood about the chemical kinetics underlying the VPI process. The aim of this study is to create a greater understanding of the process kinetics that govern the infiltration of trimethyl aluminum (TMA) and TiCl4 into PMMA to form inorganic-PMMA hybrid materials. To gain insight, this paper initially examines the predicted results for the spatiotemporal concentrations of inorganics computed from a recently posited reaction-diffusion model for VPI. This model provides insight on how the Damköhler number (reaction versus diffusion rates) and non-Fickian diffusional processes (hindering) that result from the material transforming from a polymer to a hybrid can affect the evolution of inorganic concentration depth profiles with time. Subsequently, experimental XPS depth profiles are collected for TMA and TiCl4 infiltrated PMMA films at 90 °C and 135 °C. The functional behavior of these depth profiles at varying infiltration times are qualitatively compared to various computed predictions and conclusions are drawn about the mechanisms of each of these processes. TMA infiltration into PMMA appears to transition from a diffusion-limited process at low temperatures (90 °C) to a reaction-limited process at high temperatures (135 °C) for the film thicknesses investigated here (200 nm). While TMA appears to fully infiltrate these 200 nm PMMA films within a few hours, TiCl4 infiltration into PMMA is considerably slower, with full saturation not occurring even after 2 days of precursor exposure. Infiltration at 90 °C is so slow that no clear conclusions about mechanism can be drawn; however, at 135 °C, the TiCl4 infiltration into PMMA is clearly a reaction-limited process, with TiCl4 permeating the entire thickness (at low concentrations) within only a few minutes, but inorganic loading continuously increasing in a uniform manner over a course of 2 days. Near-surface deviations from the uniform-loading expected for a reaction-limited process also suggest that diffusional hindering is high for TiCl4 infiltration into PMMA. These results demonstrate a new, ex situ analysis approach for investigating the rate-limiting process mechanisms for vapor phase infiltration.

RuO2-decorated CsxWO3 composite nanorods as transparent photothermal negative electrode material for enhancing supercapacitor performance in acid electrolyte

With the development of wearable and portable electronics, flexible transparent photothermal supercapacitors which improve the performance via the utilization of sunlight have received increasing attention. The high performance electrode materials, particularly those for negative electrodes in acid electrolytes, are needed. Herein, we developed a novel flexible transparent photothermal supercapacitor using RuO2-decorated CsxWO3 nanorods as the negative electrode material for acid electrolytes. It was demonstrated that the resulting electrodes possessed good pseudocapacitive performance in the potential window of −0.5–0.0 V in 1 M H2SO4 and the appropriate decoration of RuO2 on CsxWO3 nanorods could raise the pseudocapacitance effectively. Also, the fabricated all-solid-state supercapacitor was shown to possess high visible light transparency, flexibility, capacitive performance and stability. Its electrochemical performances could be remarkably enhanced by simulated sunlight illumination because the photothermal conversion-induced temperature increase might reduce the electrolyte and charge-transfer resistances effectively. Further kinetic analysis revealed that the enhanced capacitance was contributed by both the diffusion-limited and surface-limited processes. Accordingly, the strategy to improve the capacitive performance of CsxWO3 nanorods by RuO2 decoration was successful and made the resulting composite have great potential as the negative electrode material for transparent photothermal supercapacitors.

How to estimate isotope fractionations of a Rayleigh-like but diffusion-limited disequilibrium process?

How to estimate isotope fractionations of a Rayleigh-like but diffusion-limited disequilibrium process?

Dendritic Self-assembled Structures from Therapeutic Charged Pentapeptides.

CRENKA [Cys-Arg-(NMe)Glu-Lys-Ala, where (NMe)Glu refers to N-methyl-Glu], an anti-cancer pentapeptide that induces prostate tumor necrosis and significant reduction in tumor growth, was engineered to increase the resistance to endogenous proteases of its parent peptide, CREKA (Cys-Arg-Glu-Lys-Ala). Considering their high tendency to aggregate, the self-assembly of CRENKA and CREKA into well-defined and ordered structures has been examined as a function of peptide concentration and pH. Spectroscopic studies and atomistic molecular dynamics simulations reveal significant differences between the secondary structures of CREKA and CRENKA. Thus, the restrictions imposed by the (NMe)Glu residue reduce the conformational variability of CRENKA with respect to CREKA, which significantly affects the formation of well-defined and ordered self-assembly morphologies. Aggregates with poorly defined morphology are obtained from solutions with low and moderate CREKA concentrations at pH 4, whereas well-defined dendritic microstructures with fractal geometry are obtained from CRENKA solutions with similar peptide concentrations at pH 4 and 7. The formation of dendritic structures is proposed to follow a two-step mechanism: (1) pseudo-spherical particles are pre-nucleated through a diffusion-limited aggregation process, pre-defining the dendritic geometry, and (2) such pre-nucleated structures coalesce by incorporating conformationally restrained CRENKA molecules from the solution to their surfaces, forming a continuous dendritic structure. Instead, no regular assembly is obtained from solutions with high peptide concentrations, as their dynamics is dominated by strong repulsive peptide-peptide electrostatic interactions, and from solutions at pH 10, in which the total peptide charge is zero. Overall, results demonstrate that dendritic structures are only obtained when the molecular charge of CRENKA, which is controlled through the pH, favors kinetics over thermodynamics during the self-assembly process.

Limit Theorems for Iterates of the Szász–Mirakyan Operator in Probabilistic View

The Szász–Mirakyan operator is known as a positive linear operator which uniformly approximates a certain class of continuous functions on the half line. The purpose of the present paper is to find out limiting behaviors of the iterates of the Szász–Mirakyan operator in a probabilistic point of view. We show that the iterates of the Szász–Mirakyan operator uniformly converge to a continuous semigroup generated by a second-order degenerate differential operator. A probabilistic interpretation of the convergence in terms of a discrete Markov chain constructed from the iterates and a limiting diffusion process on the half line is captured as well.

Grain boundary metal–insulator transitions in polycrystalline LiCoO[formula omitted

A thermodynamically consistent variational framework is developed to show that the metal–insulator transition in polycrystalline LiCoO2 is driven by grain boundary lithium segregation, the interfacial misorientation, and the size of the abutting grains. In general, high-angle grain boundaries and grains possessing high curvature favor phase transformation to Li-rich phases. In particular, the insulating O3(I) phase wets high-angle grain boundaries in a manner analogous to grain boundary premelting, at least Δc=0.15 before the O3(II)-O3(I) equilibrium phase boundary, c=0.75. A critical misorientation as a function of the macroscopic lithium content, Δθc(c) exists above which the grain boundaries undergo a metal-insulating transition. The critical misorientation decreases with composition until at c=0.81, the percolation threshold is reached, forming an insulating grain boundary network that dramatically suppresses the electrical conductivity of polycrystalline LCO. The O3(I) phase extends into the O3(II) grain interiors through a diffusion-limited process, while the O3(II) phase extends into the H1-3 grain interiors through a phase transformation limited process. Results suggest that the fabrication of textured LCO microstructures will delay the metal–insulator transition. Specifically, textured microstructures exhibiting grain boundary misorientations Δθ<6∘ will suppress the formation of the insulating O3(I) phase up to the O3(II)-O3(I) phase boundary, enabling the use of an additional 64.6 Wh/kg in specific energy density and 16.4 Ah/kg of charge between c=0.75 and c=0.81.