A Hierarchical Model for Longitudinal and IntraparticleDiffusion Coefficients in Liquid Chromatography

Because in the catalyst layers (CLs) of polymer electrolyte fuel cells (PEFCs) platinum (Pt) is used as catalyst, we need to reduce the amount of Pt for cost reduction. In order to maintain the same output even when the amount of Pt is reduced, it is necessary to increase the current density per unit area of Pt surface. At high current density, mass transport is a major factor in voltage drop. Therefore, improving the oxygen transport properties in CLs will lead to cost reduction of PEFCs. Although the transport properties of oxygen in the porous structure of CLs have been studied, the effect of surface diffusion, which is the motion of an oxygen molecule on the ionomer thin film, on transport properties has not yet been clarified. The purpose of the present study is to analyze how the motion of an oxygen molecule on the ionomer thin film affects the oxygen transport properties in the CLs of PEFCs.We used the direct simulation Monte Carlo (DSMC) method. In this study, a computational system was constructed based on an actual catalyst layer sample. The three dimensional structure of the sample was obtained as sequential slice images using a focused ion beam-scanning electron microscope (FIB-SEM). In order to examine the effect of surface diffusion on the transport properties of oxygen molecules, the simulation was performed using a various conditions of the surface diffusion. The behavior of surface diffusion was determined by a surface diffusion coefficient (D s) and a time constant (τ).Figure 1 shows the results of the effective diffusion coefficient of oxygen in the CL. The red line shows the effective diffusion coefficient of oxygen in the calculation without considering the surface diffusion, which is 2.75×10-6 m2/s. The plot marks shows the each surface diffusion coefficient. As the surface diffusion coefficient increases, the effective diffusion coefficient of oxygen increases. When the surface diffusion coefficient is small, the increase in the time constant results in the decrease in the effective diffusion coefficient of oxygen. When surface diffusion coefficient is large, the increase in the time constant leads to the larger effective diffusion coefficient of oxygen. However, when the surface diffusion coefficient is large, as the time constant increases, the effective diffusion coefficient of oxygen has a peak value and then decreases. Although the surface diffusion coefficient becomes larger, the effective diffusion coefficient does not continue to increase. This trend occurs presumably due to the tortuosity of the three dimensional structure. When an oxygen molecule moves along the bended three dimensional structure, the distance of the motion of the oxygen molecule become larger than the straight-line distance between the start and end points. This is the reason why the effective diffusion coefficient does not continue to increase.Fig. 1: Effective diffusion coefficient of oxygen in the catalyst layer as a function of the time constant of the surface diffusion. The difference in plot marks shows the difference in the surface diffusion coefficient. The red line shows the effective diffusion coefficient of oxygen in the calculation without considering the surface diffusion. Figure 1

SummaryThe complex pore structure and storage mechanism of organic-rich ultratight reservoirs make the hydrocarbon transport within these reservoirs complicated and significantly different from conventional oil and gas reservoirs. A substantial fraction of pore volume in the ultratight matrix consists of nanopores in which the notion of viscous flow may become irrelevant. Instead, multiple transport and storage mechanisms should be considered to model fluid transport within the shale matrix, including molecular diffusion, Knudsen diffusion, surface diffusion, and sorption. This paper presents a diffusion-based semianalytical model for a single-component gas transport within an infinite-acting organic-rich ultratight matrix. The model treats free and sorbed gas as two phases coexisting in nanopores. The overall mass conservation equation for both phases is transformed into one governing equation solely on the basis of the concentration (density) of the free phase. As a result, the partial differential equation (PDE) governing the overall mass transport carries two newly defined nonlinear terms; namely, effective diffusion coefficient, De, and capacity factor, Φ. The De term accounts for the molecular, Knudsen, and surface diffusion coefficients, and the Φ term considers the mass exchange between free and sorbed phases under sorption equilibrium condition. Furthermore, the ratio of De/Φ is recognized as an apparent diffusion coefficient Da, which is a function of free phase concentration. The nonlinear PDE is solved by applying a piecewise-constant-coefficient technique that divides the domain under consideration into an arbitrary number of subdomains. Each subdomain is assigned with a constant Da. The diffusion-based model is validated against numerical simulation. The model is then used to investigate the impact of surface and Knudsen diffusion coefficients, porosity, and adsorption capacity on gas transport within the ultratight formation. Further, the model is used to study gas transport and production from the Barnett, Marcellus, and New Albany shales. The results show that surface diffusion significantly contributes to gas production in shales with large values of surface diffusion coefficient and adsorption capacity and small values of Knudsen diffusion coefficient and total porosity. Thus, neglecting surface diffusion in organic-rich shales may result in the underestimation of gas production.

Analysis of mass transport models based on Maxwell–Stefan theory and Fick's law for protein uptake to porous anion exchanger

Experimental study on mass transport mechanism in poly (styrene-co-divinylbenzene) microspheres with hierarchical pore structure

The surface diffusion properties of liquid silicon play a critical role in applications, such as semiconductor manufacturing and nanotechnology. Using molecular dynamics (MD) simulations based on two different popular empirical potentials, this study investigates the surface and bulk diffusion coefficients of liquid silicon. First-principle molecular dynamics simulation is also applied to provide validations. Results reveal that the size effect of the diffusion coefficient in the cubic system with surfaces will deviate from the theoretical relation (i.e., it decreases linearly with 1/L) to lower values. This effect is caused by an unusual phenomenon: the surface diffusion coefficients are lower than the bulk diffusion coefficients in liquid silicon, contrary to typical trends in other materials. This phenomenon is explained by analyzing the microstructure of the liquid surface including coordination number (CN) distributions and atomic mobility heterogeneity.

Crushing analysis and optimization for bio-inspired hierarchical 3D cellular structure

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

Hard carbon has attracted great attention for energy storage owing to low cost and extremely high microporosity, however, hindered by its low electrical conductivity. The common strategy to improve the conductivity is through graphitization process which requires temperatures as high as 3000 °C and inevitably destroys the porous structure. Herein, a balance between the specific surface area and electrical conductivity in a 3D porous hard carbon by in situ iron‐catalyzed graphitization process together with the Si–O–Si network is successfully achieved. The Fe can accelerate the localized graphitization at relatively low temperature (1000 °C) to form nanographite domains with enhanced conductivity, while the Si–O–Si network contributes to generating a 3D porous structure. As a result, the optimized hard carbon exhibits a 3D interconnected and hierarchical porous structure with extremely high specific surface area (2075 m2 g−1) and excellent electrical conductivity (12 S cm−1) which is comparable with that of artificial graphite. And thus, high capacitance of 315 F g−1 and excellent rate capability (174 F g−1 at 40 A g−1) are simultaneously achieved when used as electrodes for supercapacitors. The strategy is promising to build hard carbon materials with well‐tuned properties for high‐performance energy storage.

Preparation of novel 3D hierarchical porous carbon membrane as flexible free-standing electrode for supercapacitors

Template-free synthesis of a novel porous g-C3N4 with 3D hierarchical structure for enhanced photocatalytic H2 evolution

The electrochemical applications of traditional carbon nanomaterials such as carbon nanotubes (CNTs) and graphene (G) powders are significantly impeded by their poor three-dimensional (3D) conductivity and lack of hierarchical porous structure. Here, we have constructed a 3D highly conductive CNTs networks and further combined it with mesoporous carbon (mC) for the creation of a core-shell structured (CNT@mC) composite sponge that featured 3D conductivity and hierarchical porous structure. In the composite sponge, interconnected CNTs efficiently eliminates the contact resistance and the hierarchical pores significantly facilitate the mass transport. The electron transfer rates, electroactive surface area and catalytic activity of the CNT@mC composite sponge based catalysts were tested in the direct methanol fuel cells (DMFCs) and electrochemical sensors. In DMFCs, the Pd nanoparticles deposited CNT@mC showed significantly improved catalytic activity and methanol oxidization current. As for amperometric sensing of endocrine disrupting compounds (EDCs), CNT@mC-based catalyst gave a liner range from 10 nM to 1 mM for bisphenol A (BPA) detection and showed great promise for simultaneous detection of multiple EDCs. BPA recovery from environmental water further indicated the potential practical applications of the sensor for BPA detection. Finally, the electrochemical performance of CNT@mC were also investigated in impedimetric sensors. Good selectivity was obtained in impedimetric sensing of BPA and the detection limit was measured to be 0.3 nM. This study highlighted the exceptional electrochemical properties of the CNT@mC composite sponge enabled by its 3D conductivity and hierarchical porous structure. The strategy described may further pave a way for the creation of novel functional materials through integrating multiple superior properties into a single nanostructure for future clean energy technologies and environmental monitoring systems.

Kelp-derived three-dimensional hierarchical porous N, O-doped carbon for flexible solid-state symmetrical supercapacitors with excellent performance

A hierarchical porous polymer film that can provide a balance of mechanical properties and specific surface areas and sustain cell functions has become a major target for material scientists and bioengineers in the past decade. However, the limited availability of materials that exhibit high mechanical performance and easily form hierarchical porous structures hinder the progress in practical application. Here, we show the design of a polyhedral oligomeric silsesquioxane (POSS) hybrid polymer by incorporating a bi-functional glycidyl-propyl POSS (G-POSS) into the epoxy polymer backbone, in which POSS functions as both a nanofiller to reinforce the mechanical performance and as the polarity mediator to induce self-assembly of the polymer chains into a three-dimensional (3D) connected porous structure. Nanoindentation shows that the incorporation of POSS leads to a 25 and 36% increase in modulus and hardness, respectively. Scanning electron microscopy results show that POSS helps tune the hydrophobicity of the polymer and assists in the interface assembly, allowing easy formation of a densely packed two-dimensional or 3D hierarchical porous structure. Culture of mouse embryonic fibroblast cells demonstrates that the hybrid polymer scaffold provides prominent advantages ranging from enhanced cell adhesion to proliferation. Particularly, the 3D hierarchical porous film allows good nutrient supply and cell communication, which better mimics the in vivo microenvironment with less cell morphology change during cell proliferation. Hence, the successful integration of high material strength and easy formation of an interconnected porous structure shows that POSS hybrid polymers have strong potential for applications in the fabrication of cell culture platforms and future translation in tissue repair and regeneration.

Hierarchical porous structure construction for highly stable self-supporting lithium metal anode

Surface diffusion of organic vapor mixtures through porous glass