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Tobacco mosaic virus is used as a probe to measure surface diffusion of ultrathin films of N,N′-Bis(3-methylphenyl)-N,N′-diphenylbenzidine (TPD) (12 nm < h < 53 nm, where h is the film thickness) at various temperatures below the glass transition temperature, Tg, of all films. As the film thickness is decreased, Tg decreases rapidly and the average film dynamics are enhanced by 6–14 orders of magnitude. We show that the surface diffusion is invariant of the film thickness decrease and the resulting enhanced overall mobility. The values of the surface diffusion coefficient and its temperature dependence are invariant of film thickness and are the same as the corresponding bulk values (h = 400 nm). For the thinnest films (h < 20 nm), the effective activation energy for rearrangement (temperature dependence of relaxation times) becomes smaller than the activation energy for surface diffusion. These results suggest that the fast surface diffusion is decoupled from film relaxation dynamics and is a solely free surface property.

The time instant—the first-passage time (FPT)—when a diffusive particle (e.g., a ligand such as oxygen or a signalling protein) for the first time reaches an immobile target located on the surface of a bounded three-dimensional domain (e.g., a hemoglobin molecule or the cellular nucleus) is a decisive characteristic time-scale in diverse biophysical and biochemical processes, as well as in intermediate stages of various inter- and intra-cellular signal transduction pathways. Adam and Delbrück put forth the reduction-of-dimensionality concept, according to which a ligand first binds non-specifically to any point of the surface on which the target is placed and then diffuses along this surface until it locates the target. In this work, we analyse the efficiency of such a scenario and confront it with the efficiency of a direct search process, in which the target is approached directly from the bulk and not aided by surface diffusion. We consider two situations: (i) a single ligand is launched from a fixed or a random position and searches for the target, and (ii) the case of ‘amplified’ signals when N ligands start either from the same point or from random positions, and the search terminates when the fastest of them arrives to the target. For such settings, we go beyond the conventional analyses, which compare only the mean values of the corresponding FPTs. Instead, we calculate the full probability density function of FPTs for both scenarios and study its integral characteristic—the ‘survival’ probability of a target up to time t . On this basis, we examine how the efficiencies of both scenarios are controlled by a variety of parameters and single out realistic conditions in which the reduction-of-dimensionality scenario outperforms the direct search.

Water pollution because of the presence of heavy metals remains a serious worry. The present work demonstrates the exclusion of cobalt ion (or Co(II)) from water using novel and cost-effective biosorbents. Initially, the biosorbent was chemically modified using orthophosphoric acid and then subjected to calcination to result acid modified date seed biochar (AMDB). Three biosorbents (AMDB400, AMDB500, and AMDB600) were synthesized concerning different activation temperatures (400, 500, and 600 °C). The maximum biosorption of Co(II) was achieved on AMDB600 (149.5 mg/g), followed by AMDB500 (138.33 mg/g), and ADMB400 (129.17 mg/g). For all three biosorbents, the Co(II) removal remained effective within 50–100 min; later it reached saturation. The kinetic analysis suggested strong Co(II) adsorption on AMDB surfaces. The Co(II)-AMDB biosorption data fits well with Temkin isotherm, indicating the heterogeneity on the biosorbent surface and no interaction between adsorbed Co(II)-Co(II) species. The thermodynamic analysis suggested the exothermic and spontaneous adsorption. The intraparticle diffusion of Co(II) within the biosorbent was surface diffusion controlled, as characterized by pore volume and surface diffusion model. The biosorbent reusability was 88.7% after five adsorption–desorption cycles. Thus, presently synthesized biosorbent could be novel and cost-effective for Co(II) and other heavy metal elimination from water bodies. Graphical Abstract

Desulfurization of organosulfur compounds in petrochemical fuels is mainly limited by diffusion in porous solids. Design and optimization of such heterogeneous process need basic knowledge of molecular diffusion inside porous solids. In this work, molecular dynamics method was applied to study the intrinsic pore diffusion and surface diffusion of some common organosulfur compounds of thiophene, benzothiophene and dibenzothiophene in silica pores. Based on the molecular dynamics data, the effects of temperature and pore size on the intrinsic pore diffusion and surface diffusion were investigated by an established mathematic model considering the molecular size effect on diffusion. It was found that the widely used Knudsen diffusion model might overestimate the pore diffusion as much as a few dozens folds, but could be improved by incorporating molecular interaction and molecular size effect into diffusion model. The proportion of mass transfer by surface diffusion in total mass transfer in different pores was estimated. The results exhibited herein convey some basic instruction not only for design pores of porous solids used in hydrodesulfurization or in adsorption desulfurization, but also for optimization of operation conditions for desulfurization processes.

In this work, convective–dispersive and pore volume and surface diffusion models have been used to analyze Pb(II) adsorption from an aqueous solution over a nanostructured γ-alumina adsorbent in a packed bed adsorber. The models encompassing partial differential equation and a linear algebraic equation coupled with isotherm have been simulated in gPROMS using the backward finite difference approach. The predicted breakthrough curves of Pb(II) adsorption concerning flow rate, initial metal concentration, and bed height were matched with the experimental data. The accuracy of model predictions was analyzed through statistical measures such as coefficient of determination ( R 2 ), root mean square error, and chi-squared value. The simulation results also predicted the axial dispersion, distribution coefficient, mass transfer coefficient, pore volume, and surface diffusion coefficient, which are, otherwise, difficult to measure experimentally and, in turn, have been used to assess the mass transfer characteristics of continuous Pb(II) adsorption. Additionally, the values of breakthrough time, exhaustion time, adsorption column capacity, and mass transfer zone were determined as a function of flow rate, bed height, and initial metal concentration. Surface and pore volume diffusions (10 −11 –10 −10 m 2 /s) apparently controlled the continuous adsorption process, with surface diffusion being dominant. The transport parameters evaluated in the current study could be beneficial for the large-scale Pb(II)/nanostructured γ-alumina adsorption system. As evident from the successful simulation, the developed gPROMS program can also be applied to other adsorbate/adsorbent systems with a slight modification concerning the operating parameters.

The theory of mass transport in porous media is of fundamental importance for different applications such as food, paper packaging, textiles, and wood for building materials. In this study, a theoretical water vapor transport model has been developed for cellulose-based materials, such as paper and regenerated cellulose film. Pore diffusivities were determined from the dynamic moisture breakthrough experiments comprising a stack of paper sheets and regenerated cellulose films in a configuration similar to a packed adsorption column. Other mass transfer parameters were determined from transient moisture uptake rate measurements. The model incorporates pore and surface diffusion as a lump parameter into a variable effective diffusion coefficient. The mass transport, involving both pore and surface diffusions, is evaluated independently. The theoretical water vapor transmission rates (WVTRs) obtained from the model were compared with experimentally determined WVTRs measured under steady-state conditions. The theoretical model, based on intrinsic diffusion, stipulates higher WVTR values compared to the experimental results. However, the theoretical water vapor transfer rates agree well with the experimental results when external mass transfer resistance is incorporated in the model.

This paper presents the results of adsorption and permeation experiments of hydrogen and methane at elevated temperatures on a carbon-based nanoporous membrane material provided by Fraunhofer IKTS. The adsorption of pure components was measured between 90 °C and 120°C and pressures up to 45 bar. The Langmuir adsorption isotherm shows the best fit for all data points. Compared to available adsorption isotherms of H2 and CH4 on carbon, the adsorption on the investigated nanoporous carbon structures is significantly lower. Single-component permeation experiments were conducted on membranes at temperatures up to 220 °C. After combining the experimental results with a Maxwell–Stefan surface diffusion model, Maxwell–Stefan surface diffusion coefficients Dis were calculated. The calculated values are in line with an empirical model and thus can be used in future multi-component modeling approaches in order to better analyze and design a membrane system. The published adsorption data fill a gap in the available adsorption data for CH4 and H2.

The phase formation of PtIrCuAuX (X = Ag, Pd) compositionally complex thin films is investigated to critically appraise the criteria employed to predict the formation of high entropy alloys. The formation of a single-phase high entropy alloy is predicted if the following requirements are fulfilled: 12 J∙K−1 mol−1 ≤ configurational entropy ≤ 17.5 J∙K−1 mol−1, −10 kJ∙mol−1 ≤ enthalpy of mixing ≤ 5 kJ∙mol−1 and atomic size difference ≤ 5%. Equiatomic PtIrCuAuX (X = Ag, Pd) fulfill all of these requirements. Based on X-ray diffraction and energy-dispersive X-ray spectroscopy data, near-equiatomic Pt22Ir23Cu18Au18Pd19 thin films form a single-phase solid solution while near-equiatomic Pt22Ir23Cu20Au17Ag18 thin films exhibit the formation of two phases. The latter observation is clearly in conflict with the design rules for high entropy alloys. However, the observed phase formation can be rationalized by considering bond strengths and differences in activation energy barriers for surface diffusion. Integrated crystal orbital Hamilton population values per bond imply a decrease in bond strength for all the interactions when Pd is substituted by Ag in PtIrCuAuX which lowers the surface diffusion activation energy barrier by 35% on average for each constituent. This enables the surface diffusion-mediated formation of two phases, one rich in Au and Ag and a second phase enriched in Pt and Cu. Hence, phase formation in these systems appears to be governed by the complex interplay between energetics and kinetic limitations rather than by configurational entropy.

A method to model the metastable phase formation in the Cu-W system based on the critical surface diffusion distance has been developed. The driver for the formation of a second phase is the critical diffusion distance which is dependent on the solubility of W in Cu and on the solubility of Cu in W. Based on comparative theoretical and experimental data, we can describe the relationship between the solubilities and the critical diffusion distances in order to model the metastable phase formation. Metastable phase formation diagrams for Cu-W and Cu-V thin films are predicted and validated by combinatorial magnetron sputtering experiments. The correlative experimental and theoretical research strategy adopted here enables us to efficiently describe the relationship between the solubilities and the critical diffusion distances in order to model the metastable phase formation during magnetron sputtering.

We study in this work the growth of a gold monolayer on a Cu (110) surface thanks to the kinetic Monte Carlo method. We considered a coverage of 0.1% of the monolayer. Indeed, the growth of a monolayer is done through the intermediary of several diffusion processes. All activation energies for each process were calculated using the static method coupled with the KMC method. This coupling is established by the ABBM anisotropic bond breaking model. The study of the results obtained in the temperature range (100-300K) at different deposition rates shows the formation of small 1D islands and certain 2D islands at high temperature (280 k-300 K).