Surface Diffusion Coefficient Research Articles

Diffusion behavior of rhodamine 6G in single octadecylsilyl-functionalized silica particle revealed by fluorescence correlation spectroscopy.

We investigated the diffusion behavior of rhodamine 6G (Rh6G) within single octadecylsilyl-functionalized (ODS) silica particle in an acetonitrile (ACN)/water system using fluorescence correlation spectroscopy (FCS). FCS measurements were conducted at the center of the particle to exclusively determine the intraparticle diffusion coefficient (D). The obtained D values were analyzed based on a pore and surface diffusion model, the results of which indicate that surface diffusion primarily governs the intraparticle diffusion of Rh6G. Furthermore, an increase in the concentration of ACN (CACN) resulted in a corresponding increase in the surface diffusion coefficient (Ds), whereas the addition of NaCl did not significantly affect the Ds values. We attributed this dependence of Ds to the dielectric constant change in the interfacial liquid phase formed on the ODS layer. Specially, Ds values of (4.0 ± 0.5) × 10-7, (7.7 ± 1.1) × 10-7, (1.0 ± 0.3) × 10-6, and (1.1 ± 0.2) × 10-6cm2s-1 were obtained for CACN = 20, 30, 40, and 50vol%, respectively. We anticipate that this approach will contribute to advancing research on intraparticle mass transfer mechanisms.

Selection of Optimum Ternary Binder Systems that Enhance the Workability and Durability of Concrete used in Marine Railways

In this study, the improvement of the compressive strength and duradbility of concrete used in marine railways by adding binding agents was investigated. The test speciments used in the study comprised developed product A (DP_A), developed product B (DP_B), Ordinary Portland Cement (OPC), admixture A, and admixture B, in the study, the optimum ternary binder systems of the test specimens were identified. An optimum ternary binder system would facilitate the simultaneous enhancement of the durability and workability of concrete used on undersea tunnel linings and bridge structures. The compressive strength of each specimen tested after 16h could easily meet the specified standard target strength (> 3.0_MPa). Moreover, the 7d long term strength of each test specimen exceeded 3.0 MPa. When binders were used, the chloride penetration resistance (DP_A was exceptional)_2.741C (normal) and, 1.490C (low) following-28 and 91days. The surface diffustion coefficient of (DP_B) at 91days 9.12 (× 10-12, m<sup>2</sup>/sec) was higher than that of OPC 9.55 (× 10-12, m<sup>2</sup>/sec). However, the surface diffusion coefficient of (DP_A) was 4.15 (× 10-12, m<sup>2</sup>/sec) which was lower than OPC by approximately 57%, indicating the outstanding durability of DP_A.

Insight into Adsorption Kinetics of Cs+, Rb+, Co2+, and Sr2+ on a Zeolites-Based Composite: Comprehensive Diffusional Explanation and Modelling

Kaolinite-rich soils were used to prepare zeolite-based composites via alkaline activation. The porous material was characterized by conducting XRD and microporosity measurements, as well as ESEM microscopy. The Weber and Morris (W-M) model was used for studying adsorption kinetics of radioactive cations on synthesized alkali-activated material. These investigations evidenced the effects of pore structure and the importance of the intrinsic characteristics of hydrated cations (ionic potential; hydrated radius; B-viscosity parameter; molar Gibbs energy of hydration of cation) on W-M kinetic rate constants. The application of diffusion-based models permitted us to assess the key diffusion parameters controlling successive diffusion regimes, and to reveal strong contributions of surface diffusion to adsorption kinetics during the course of the second and third kinetics stages of the W-M model. The magnitude of the surface diffusion coefficient was related to the capacity of hydrated cationic species to lose water molecules when penetrating brick pores. The HSDM model were tested for predicting radionuclide adsorption in a fixed-bed column. A breakthrough curve simulation indicated the predominance of the surface diffusion regime, which was in agreement with mathematical analysis of (batch) adsorption kinetics data. Ionic diffusion was linked to the characteristics of capillary porosity and connectivity of capillary pores in the composite, suggesting the generation of hydrated nuclides and their immobilization in the form of outer-sphere complexes.

Influence of (1 1 1) texture on bonding strength in low-temperature bonding of nanotwinned Ag films: Experimental insights and void closure modeling

Low-temperature bonding of nanotwinned (NT-) metals holds great potential for enhancing the performance and reliability of electronic interconnections. In this study, we performed low-temperature bonding of (111)-oriented nanotwinned silver (NT-Ag) films and thoroughly investigated the influence of (111) texture on the interfacial microstructure and bonding strength of the joints. The results demonstrated that high-quality bonding of highly (111)-oriented NT-Ag films was achieved even at 200 °C in air. The defect-free, coherent Ag(111)Ag(111) bonding interface was formed via face-to-face bonding of the highly (111)-oriented columnar grains. The shear strength of the joints significantly increased with the rise in (111) texture intensity. Moreover, we developed the void closure model to quantitatively elucidate the contribution of (111) texture to void closure and bonding ratio. Modeling results revealed that the (111) texture, with the highest surface diffusion coefficient, greatly increased the interfacial bonding ratio by accelerating surface source diffusion, thereby enabling high-strength bonding at low temperatures. The experimental validation and modeling results presented here contribute a novel perspective for optimizing interfacial microstructure and bonding strength by regulating the surface texture in the solid-state bonding of metals.

Surface diffusion on a palladium-based metallic glass

The surface diffusion kinetics on a Pd77.5Cu6Si16.5 metallic glass is measured using a scratch smoothing method in the range of 107–57 K below the glass transition temperature. Within this temperature range, the surface diffusion coefficients are determined to vary between (8.66 ± 0.80) × 10−19 and (5.90 ± 0.60) × 10−18 m2 s−1. The corresponding activation energy is 0.93 ± 0.18 eV, which is about half the value for bulk diffusion. These measurements also corroborate the correlation between enhanced surface diffusion and liquid fragility in glasses.

Ag Surface Outflow Kinetics in Ag/AlN Nanomultilayers

The heat‐induced microstructure evolution of nanomultilayers (NMLs) with metallic components is widely studied due to its critical importance in ensuring the reliable application of these nanomaterials. The thermal degradation of NMLs is controlled by mass transport of one of the NML components from the NML volume to its surface. The outflow occurs at temperatures well below the melting point of metal, offering new opportunities for the engineering of innovative NML‐based brazing fillers. A combined experimental‐modeling approach for the quantitative analysis of silver (Ag) outflow kinetics in Ag/AlN NMLs is presented. The method is based on in situ monitoring of the X‐ray diffraction intensity evolution of Ag acquired from the near‐surface region of NML (grazing incidence geometry) upon annealing in the temperature range of 230–425 °C (atmosphere of N2). The experimental data are compared to model predictions of Ag diffusion. It is assumed that Ag diffusion is driven by the relaxation of residual stresses in Ag nanolayers. Due to the multilayer geometry, the surface outflow kinetics are mainly defined by the kinetics of Ag diffusion along Ag/AlN interphase boundaries. The parameters defining the Ag surface outflow kinetics, i.e., diffusion coefficients and activation energy for diffusion, are derived.

Nanoporous gold with microporous structure prepared by sodium dodecyl sulfate-mediated electrochemical dealloying

Nanoporous gold (NPG) is a promising catalytic material for the oxidation of CO and methanol applications. However, NPGs are prone to extensive macroscopic cracking that often decrease mechanic properties of NPGs and depresses their catalytic action. To produce crack-free NPG with an ultra-finer porosity in room temperature, the anionic surfactant sodium dodecyl sulfate (SDS) was added in electrochemical dealloying process. SDS has the effect of reducing the surface diffusion of gold which hinder the initial coarsening of ligaments and prevents interior silver atoms from being exposed and dissolved. As a result, the pore and ligment size are finer, but higher residual silver of NPG samples. NPG with pore size down to 2 nm and the ligament 4.0 nm was successfully fabricated with 13.32 mM SDS in perchloric acid solution. The surface diffusion coefficient of Au atoms was 1.6 × 10−24 m2·s−1, nearly 3 orders of magnitude smaller than that of Au atoms in the absence of SDS (2.8 × 10−21 m2·s−1). Nanoindentation results demonstrated that high residual silver content made NPG samples harder and stiffer，the specific surface areas of NPG with 6.66 mM SDS was 190 m2 g−1 by BET. This work provided very important clues on how to control the crack free ultrafine nanoporous structure of other materials.

Coupled model on the variation of diffusion coefficient and surface chloride concentration in reinforced concrete structures over time

Durability analyses and service life estimates of structures in a marine environment can be developed through the modeling of chloride concentration profiles. However, as surface chloride concentration and diffusion coefficient vary over time, especially due to the cement hydration process, modeling chloride profiles from structures with recent degradation ages requires an adjustment for the temporal dependence of these two physical parameters. The variation of the surface chloride concentration (Cs) as a function of time tends to show an increasing asymptotic behavior, while the diffusion coefficient (D) has a decreasing asymptotic tendency. For this reason, the power function, usually used to describe the diffusion coefficient, has problems for advanced ages, while the exponential function has difficulties at recent ages. Therefore, the key issue in this problem is the rate of change of Cs and D over time. This article presents the development of a single time-dependence model to simultaneously describe the decrease in D and the increase in Cs over time. The coupled model is a piecewise-defined function, with continuity of the function and its first derivative in the transition time between recent ages and more advanced ages, defined as 10 years. To validate the new model, data from structures under natural degradation were used. The results demonstrated the applicability of the coupled model with individual adjustments of the exponent α, which implicitly represents material properties and environmental parameters. However, in the absence of sufficient information, a standard α exponent of 0.25 per year can be adopted, demonstrating a moderate to strong adherence of the coupled model to the Cs and D data over time. Three stages of temporal dependence were identified: I – up to 10 years: marked increase in Cs and decrease in D over time; II – between 10 and 25 years: decrease in the variation rate of Cs and D; and III – from 25 years: stabilization of Cs and D.

Molecular Dynamics Analysis of the Scattering Phenomena of Oxygen Molecules on an Ionomer Surface in Catalyst Layer of Fuel Cell

As energy demand increases and global warming progresses, expectations for fuel cells, which generate electricity through chemical reactions between hydrogen and oxygen, are rising. There are various types of fuel cells, which are classified according to the electrolyte. Polymer electrolyte fuel cells (PEFCs) are expected to be used in stationary power sources for home use and fuel cell vehicles because of their low operating temperature, short start-up time, and ease of miniaturization. The cost has been an issue in the widespread use of fuel cells. The amount of platinum used in the catalyst layer (CL) must be reduced to reduce costs. However, it increases the current density per unit area of platinum. There are three factors that contribute to voltage drop: ohmic polarization, activation polarization, and diffusion polarization. At high current densities, the voltage drop due to diffusion polarization is dominant. The main cause of diffusion polarization is the transport resistance of oxygen molecules in the CL, and improving the oxygen transport properties in the CL will lead to lower cost PEFCs. In this study, we analyzed the transport properties of oxygen molecules in the CLs of PEFCs using the Monte Carlo (MC) method. The effect of oxygen scattering on the overall oxygen transport properties was investigated by considering the behavior on the surface of the ionomer film (surface diffusion) into the MC method, which simulates the overall transport in the PEFC CL. The objective of this study is to reproduce accurate oxygen transport by comparing the results of MC and molecular dynamics (MD) methods. First, we used the MC method to analyze oxygen scattering phenomena. In this study, we used the 3D structure data of CL in the MC simulations. The three-dimensional structure of the sample was reconstructed from sequential slice images. Molecules were assumed to reflect specularly on the boundaries of the simulation domain. Oxygen molecules were randomly placed in the simulation system. The time step was set at 5 ps and the simulation time was set at 4 μs. In order to examine the effect of surface diffusion on the transport properties of oxygen molecules, the simulation was performed using various conditions of surface diffusion. We calculated the effective diffusion coefficient of oxygen in the CL as the transport property of oxygen molecules in the MC method. As the surface diffusion coefficient increases, the effective diffusion coefficient of oxygen increases. When the surface diffusion coefficient is small, the effective diffusion coefficient of oxygen increases due to a decrease in the time constant, which determines the probability distribution of the surface residence time. However, when the surface diffusion coefficient is large, a different trend emerges. As the time constant increases, the effective diffusion coefficient has a peak value and then decreases. Next, to verify the model of surface diffusion in the MC method, we analyzed the scattering phenomenon of oxygen molecules in a simulation system that simulates the pores in the CL using the MD method. We modeled the nano pores in the CL as a slit between the ionomer walls in the MD method. Nafion with the equivalent weight (EW) of 1146 was used as polymer model. The number of Nafion chains is set at 4, and the water content λ is set at 7. Three-dimensional periodic boundary conditions were applied to the simulation domain. After the system was equilibrated, 1 ns of NVT simulation was performed for production. The temperature was set at 297 K. The behavior of oxygen molecules impacting on the ionomer wall was analyzed. We analyzed the behavior of oxygen molecules colliding with the ionomer membrane using the MD method. The average residence time of surface diffusion on the ionomer thin film was of the order of 10-10s. When the calculation results were compared with the MC results, it was found that the average residence time obtained by the MD method was the value where the surface diffusion coefficient affects much on the effective diffusion coefficient. Comparing the results of the MD method with the surface diffusion model used in the MC method, there are some discrepancies between the results and the model. For example, the MC method used a model in which oxygen molecules reflect diffusively on the ionomer surface. However, in the MD method, it was found that oxygen molecules tend to reflect in the direction of travel (Fig. 1). Therefore, a more accurate model of the MC method needs to be developed in the future. Figure 1

Enhanced adsorption of bisphenol-A from water through the application of isocyanurate based hyper crosslinked resin

The widespread utility of Bisphenol A (BPA) in the production of diverse plastic substances including mineral water bottles, food packets, toys, tickets, etc. leads to its release to the environment through industrial effluents that contaminate both the surface and underground water. Given its higher toxicity and harmful effects on both human health and aquatic life, the adsorption of BPA has been the subject of recent studies at present. Herein, we disclose the synthesis of a new hyper cross-linked resin (ICYN-PPA), derived from commercially available 3,3′-(piperazine-1,4-diyl)bis(propan-1-amine) and tris(2,3-epoxypropyl) isocyanurate in a single step reaction, and its adsorptive performance for the removal of BPA from aqueous solution. The thermally stable ICYN-PPA, which is porous and exhibits different sizes of particles on its surface, displayed optimum removal of BPA. The isothermal studies were well represented by the Koble-Corrigan model, where the capacity increased from 216.6 to 228.6 mg g−1 with an increasing temperature of 318 K. The linear driving force model (LDF) was efficient in representing the kinetic data. Whereas the system tends to reach equilibrium after 350 min. The surface diffusion coefficients were 1.301 × 10−16 and 1.859 × 10−16 cm2 s−1 for BPA adsorption on isocyanurate based hyper crosslinked resins. The thermodynamic parameters confirmed the endothermic nature of the process (ΔH0 = 35.83 kJ mol−1) based on physical interactions.

Effect of Amino-Functionalized Polyhedral Oligomeric Silsesquioxanes on Structure-Property Relationships of Thermostable Hybrid Cyanate Ester Resin Based Nanocomposites.

Nanocomposites of cyanate ester resin (CER) filled with three different reactive amino-functionalized polyhedral oligomeric silsesquioxane (POSS) were synthesized and characterized. The addition of a small quantity (0.1 wt.%) of amino-POSS chemically grafted to the CER network led to the increasing thermal stability of the CER matrix by 12-15 °C, depending on the type of amino-POSS. A significant increase of the glass transition temperature, Tg (DSC data), and the temperature of α relaxation, Tα (DMTA data), by 45-55 °C of the CER matrix with loading of nanofillers was evidenced. CER/POSS films exhibited a higher storage modulus than that of neat CER in the temperature range investigated. It was evidenced that CER/aminopropylisobutyl (APIB)-POSS, CER/N-phenylaminopropyl (NPAP)-POSS, and CER/aminoethyl aminopropylisobutyl (AEAPIB)-POSS nanocomposites induced a more homogenous α relaxation phenomenon with higher Tα values and an enhanced nanocomposite elastic behavior. The value of the storage modulus, E', at 25 °C increased from 2.72 GPa for the pure CER matrix to 2.99-3.24 GPa for the nanocomposites with amino-functionalized POSS nanoparticles. Furthermore, CER/amino-POSS nanocomposites possessed a higher specific surface area, gas permeability (CO2, He), and diffusion coefficients (CO2) values than those for neat CER, due to an increasing free volume of the nanocomposites studied that is very important for their gas transport properties. Permeability grew by about 2 (He) and 3.5-4 times (CO2), respectively, and the diffusion coefficient of CO2 increased approximately twice for CER/amino-POSS nanocomposites in comparison with the neat CER network. The efficiency of amino-functionalized POSS in improving the thermal and transport properties of the CER/amino-POSS nanocomposites increased in a raw of reactive POSS containing one primary (APIB-POSS) < eight secondary (NPAP-POSS) < one secondary and one primary (AEAPIB-POSS) amino groups. APIB-POSS had the least strongly pronounced effect, since it could form covalent bonds with the CER network only by a reaction of one -NH2 group, while AEAPIB-POSS displayed the most highly marked effect, since it could easily be incorporated into the CER network via a reaction of -NH2 and -NH- groups with -O-C≡N groups from CER.

Modeling of chloride-induced corrosion in concrete bridge using the simplified and full probabilistic methods

Concrete and reinforced concrete structures are subjected to chloride corrosion, which can shorten their service life and safety of use. Reliability and safety prediction of concrete structures is a crucial task for optimizing their life cycle design and maintenance and for minimizing their life cycle costs. In the paper a probabilistic analysis of concrete durability in structural members is presented. Two methods: simplified-probabilistic and full-probabilistic have been applied for modelling chloride-induced corrosion in concrete structures. The uncertainty of the key parameters including surface chloride concentration, chloride threshold, cover depth and diffusion coefficient, which govern the chloride ingress into concrete and corrosion of reinforcing steel have been analyzed. A case study of a reinforced concrete bridge has been used to illustrate the capability and efficiency of these probabilistic methods in modeling the uncertainty and predicting the time-dependent probability of corrosion. FREeT-D and ProCAAT software have been used for the analysis.

Ultrasound-enhanced adsorption of amino acids from aqueous solution onto macroporous resins for green separation: Mass transfer mechanism and acoustic cavitation properties

The utilization of green technology for the recovery of renewable components has garnered significant attention. In this study, efficient and rapid separation of amino acids from aqueous solutions was achieved through ultrasound-assisted macroporous resin adsorption. The numerical simulation revealed the underlying mechanism of mass transfer during ultrasound-assisted adsorption and clarified the impact of acoustic properties on the adsorption process. Low-frequency (LFUS, 20 kHz) caused the damage of resin structure and the increase of adsorption capacity whereas these were less influenced by high-frequency ultrasound (HFUS, 1056 kHz). The external mass transfer coefficient was increased by 161% and 45% during LFUS- and HFUS-assisted adsorption than agitation-assisted adsorption. In addition, both US modes contributed to an enhancement of surface diffusion coefficient by over 100%. The predominant factor governing the intraparticle diffusion for amino acid adsorption was found to be pore volume diffusion, accounting for more than 70% of the overall process. Both LFUS and HFUS were observed to augment the influence of surface diffusion within the overarching diffusion phenomenon, aligning with the concurrent elevation of the surface diffusion coefficient. Furthermore, the mechanism of ultrasound-assisted adsorption was illustrated from the aspect of physical and sonochemical effects generated by the acoustic cavitation. The accumulated acoustic pressure of LFUS exceeded that of HFUS by a factor of 105, reflecting its strong physical effects. The connection between the mass transfer behaviour and acoustic bubble properties during ultrasound-assisted adsorption can provide guidance for the industry to apply ultrasound as a green technology to separate and recover renewable biomaterials from wastewater.

Comparative phenomenological modeling of the overall adsorption rate of drugs onto activated carbon. The case of the chlorpheniramine

The adsorption of chlorpheniramine on a predominantly acid-granular activated carbon was studied using diffusional kinetic models. The experiments were performed on rotatory basket batch adsorbers at pH values of 4, 7 and 9 and temperatures of 25, 35 and 45 °C using the equilibrium concentration and uptake of each experiment to describe the equilibrium behavior. The textural characterization demonstrated a type IV N2 isotherm, indicating that the active carbon used combines micro and mesopores. The adsorption isotherms obtained presented Langmuir behavior with an average deviation of 3%. The diffusional modelling revealed that surface diffusion is the predominant intraparticle diffusion mechanism governing the adsorption process, with contributions to the total intraparticle diffusion being higher than 96% regardless of the radial position. However, these contributions decreased as low as 50% when Chlorpheniramine (CPM) uptake increased. The pH studies demonstrated that the surface diffusion coefficient increased as the pH increased due to a combination of stronger π stacking interactions and electrostatic interactions. Meanwhile the temperature study demonstrated an increase in surface diffusivity as the temperature increased due to the higher energy that the chlorpheniramine molecules gained due to the temperature increment.

Three-Dimensional Mass Transfer Modeling of Hydroquinone Adsorption on Phragmites australis Biochar.

In this work, the overall adsorption kinetic process of hydroquinone on Phragmites australis biochar (PAC) was analyzed in depth. A 3D mass transfer model of pore volume and surface diffusion was established, and the diffusion mechanism was analyzed. The characterization results show PAC has a higher porosity value, which is conducive to the adsorption of hydroquinone. The adsorption process modeling results show that the combined effect of pore volume diffusion and surface diffusion promotes the total diffusion process of hydroquinone in the PAC particles, and the two mechanisms of pore volume and surface diffusion exist simultaneously. Under the different operating concentrations, the range of surface diffusion coefficient Ds is 2.5 × 10-10-1.74 × 10-9 cm2/s, and the contribution rate of surface diffusion SDCP% is close to 100%, which is much larger than pore volume diffusion, revealing that regardless of the contact time and position, surface diffusion occupies the main position in intraparticle diffusion.

Microwave drying method investigation for the process and kinetics of drying characteristics of zinc-leaching residue.

Due to the high moisture content in the zinc-leaching residue, it is easy to cause safety problems when directly entering the kiln. Microwave drying can minimize particle agglomeration and promote cracks on the mineral surface, which benefits the subsequent recovery and smelting of zinc-leaching residue. The results showed that increasing microwave power and particle size range could improve the maximum drying rate and reduce the drying time. The maximum drying rate of 20g zinc-leaching slag with a microwave power of 700 W, a particle size of 1-10mm, and a moisture content of 20% can be higher than 0.365%/s and reach complete drying within 120s. The drying results were fitted and statistically analyzed using nine common kinetic models of drying, the surface diffusion coefficient changes were further analyzed at four levels, and the reaction activation energy (Ea) was calculated. According to Fick's second law, when the average particle size increased from 0.044 to 5.5mm, the surface diffusion coefficient increased from 6.2559 × 10-9 to 3.8604 × 10-6 m2/s, which showed that the effect of particle size change on microwave drying process was significant. The Ea of the drying reaction was 18.1169kJ/mol. This method provides an idea for efficiently treating secondary resources containing valuable metals.

Adsorption and Surface Diffusion of Atomic Ru on TiN and SiO2: A First-Principles Study

Ruthenium (Ru) has been suggested as one of the promising materials for nanoscale interconnects to substitute copper (Cu) that is currently used in the semiconductor industry. Through density functional theory (DFT) calculations, we present the rationales for varying deposition behavior of Ru on different types of substrates. For the SiO2 and TiN substrates, with and without adsorbed hydrogen, our calculation results reveal the adsorption sites and their adsorption energy, the surface diffusion paths and their activation energy, and the surface diffusion coefficients. We confirm that the adsorption of Ru is more stable on TiN than on SiO2 substrates, and that the surface diffusion of Ru adatom is faster on TiN than on SiO2 surface.

Adsorption mechanism and mass transfer modeling of cesium and europium ions adsorption onto hematite-loaded polyacrylamide-gel composite: Pore Volume and Surface Diffusion Model Approach

The overall adsorption rate of cesium (Cs+) and europium (Eu3+) ions onto hematite-loaded polyacrylamide-gel composite (HPAC) in single and binary pollutant systems was explained with diffusional model that takes into consideration both external mass transfer and intra-particle diffusion. The influence of changing system temperature on the overall adsorption rate of Cs+ and Eu3+ onto HPAC was studied. The fitting process of the experimental data with the three studied isotherm models (Langmuir, Freundlich and Prausnitz–Radke (P-R)) showed that Prausnitz–Radke model has the highest correlation coefficients with the smallest average relative error percentage. The maximum P-R adsorption capacity of HPAC decreased from 2.06 and 3.35 L/g in single pollutant solution to 1.02 and 1.51 L/g in binary pollutant solution at 298 K for Cs+ and Eu3+,respectively. The values of surface diffusion coefficient (DS) ranged within 10−8 for Cs+ and 10−8-10−9 cm2/s for Eu3+ in both studied single and binary pollutant systems. The external mass transfer coefficient (KF) was in the range of 10−4 for Cs+ and 10−3 cm/s for Eu3+ in both studied systems. Lastly, the Biot number (Bi) exposed that the diffusion inside the particle controlled the studied cations's adsorption onto HPAC material.

Surface diffusion in narrow channels on curved domains.

We study the transport properties of diffusing particles restricted to confined regions on curved surfaces. We relate particle mobility to the curvature of the surface where they diffuse and the constraint due to confinement. Applying the Fick-Jacobs procedure to diffusion in curved manifolds shows that the local diffusion coefficient is related to average geometric quantities such as constriction and tortuosity. Macroscopic experiments can record such quantities through an average surface diffusion coefficient. We test the accuracy of our theoretical predictions of the effective diffusion coefficient through finite-element numerical solutions of the Laplace-Beltrami diffusion equation. We discuss how this work contributes to understanding the link between particle trajectories and the mean-square displacement.

A comparative study on surface tension, diffusion coefficient and shear viscosity coefficient of liquid transition metals

Surface tensions of liquid transition metals of the 3d, 4d and 5d series have been calculated using modified Mayer’s formula involving hard sphere (HS) interaction of liquids derived from first and second order approximations of Percus–Yevick (PY) solutions of isothermal compressibility. Effective HS diameter and packing fraction are key ingredients of this study. To determine them, we have used effective pair potential derived from both Bretonnet–Silbert (BS) pseudopotential model and many body potential obtained from embedded atom method (EAM) in conjunction with variational modified hypernetted chain (VMHNC) integral equation theory of liquid structure. Calculated values of surface tension are used to evaluate transport coefficients such as diffusion and shear viscosity coefficients. Comparing with experimental and simulated data, calculated results suggest that expression derived from second order approximation of PY solution with the combination of EAM potential and VMHNC theory works better than any other combinations for the concerned systems.