Pore structure of the packing of fine particles

This paper presents a numerical study of the pore structure of fine particles. By means of granular dynamics simulation, packings of mono-sized particles ranging from 1 to 1000 microm are constructed. Our results show that packing density varies with particle size due to the effect of the cohesive van der Waals force. Pores and their connectivity are then analysed in terms of Delaunay tessellation. The geometries of the pores are represented by the size and shape of Delaunay cells and quantified as a function of packing density or particle size. It shows that the cell size decreases and the cell shape becomes more spherical with increasing packing density. A general correlation exists between the size and shape of cells: the larger the cell size relative to particle size, the more spherical the cell shape. This correlation, however, becomes weaker as packing density decreases. The connectivity between pores is represented by throat size and channel length. With decreasing packing density, the throat size increases and the channel length decreases. The pore scale information would be useful to understand and model the transport and mechanical properties of porous media.     

Modeling growth of organized nanoporous structures by anodic oxidation

Nanostructured porous oxides are produced by anodic dissolution of several metals. A scaling approach is introduced to explain pattern nucleation in an oxide layer, and a related microscopic model shows oxide growth with long nanopores. The scaling approach matches the time of ion transport across the thin oxide layer, which is related to metal corrosion, and the time of diffusion along the oxide/solution (OS) interface, which represents the extension of oxide dissolution. The selected pattern size is of order (dD(S)/v(O))(1/2), where d is the oxide thickness, v(O) is the migration velocity of oxygen ions across the oxide, and D(s) is the diffusion coefficient of H(+) ions along the oxide/solution interface. This result is consistent with available experimental data for those quantities, predicts the increase of pore size with the external voltage, and suggests the independence of pore size with the solution pH. Subsequently, we propose a microscopic model that expresses the main physicochemical processes as a set of characteristic lengths for diffusion and surface relaxation. It shows a randomly perturbed OS interface at short times, its evolution to pore nucleation and to stable growth of very long pores, in agreement with the mechanistic scenario suggested by two experimental groups. The decrease of the size of the walls between the pores with the interface tension is consistent with arguments for formation of titania nanotube arrays instead of nanopores. These models show that pattern nucleation and growth depend on matching a small number of physicochemical parameters, which is probably the reason for the production of nanostructured porous oxides from various materials under suitable electrochemical conditions.     

Statistical analysis of packed beds,the origin of short-range disorder,and its impact on eddy dispersion

We quantified the microstructural disorder of packed beds and correlated it with the resulting eddy dispersion. For this purpose we designed a set of bulk (unconfined) monodisperse random sphere packings with a systematic, protocol-dependent degree of microstructural heterogeneity, covering a porosity range from the random-close to the random-loose packing limit (? = 0.366–0.46). With the precise knowledge of particle positions, size, and shape we conducted a Voronoï tessellation of all packings and correlated the statistical moments of the Voronoï volume distributions (standard deviation and skewness) with the porosity and the protocol-dependent microstructural disorder. The deviation of the Voronoï volume distributions from the delta function of a crystalline packing describes the origin of short-range disorder of the investigated random packings. Eddy dispersion was simulated over a wide range of reduced velocities (0.5 ≤  ν ≤ 750) and analyzed with the comprehensive Giddings equation. Transient dispersion was found to correlate with the spatial scales of heterogeneity in the packings. The analysis of short-range disorder based on the Voronoï volume distributions revealed a strong correlation with the short-range interchannel contribution to eddy dispersion, whereas transchannel dispersion was relatively little affected. The presented approach defines a strictly scientific route to the key morphology–transport relationships of current and future chromatographic supports, including their morphological reconstruction, statistical analysis, and the correlation with relevant transport phenomena. It also guides us in our understanding, comparison, and optimization of the diverse packing algorithms and protocols used in simulations and experimental studies.     

From amorphous solid to defective crystal. A study of structural peculiarities in close packings of hard spheres

The structure of models of close packings of hard spheres is examined, with density of the packings exceeding the maximum value for uniform disordered packings (η = 0.64). High densities are achieved due to regions of the closest packing (η = 0.74) emerging in the models. Spatial geometry of good tetrahedral atomic configurations and of simplest elements of the crystal structure identified by Delaunay simplices was studied using the Voronoi— Delaunay method. Models with a packing coefficient η varying from 0.639 to 0.706 were considered. At smaller densities, a well-known disordered close “Bernal packing” is realized. At η = 0.706 (the greatest density achieved), a unified crystal structure with numerous defects is formed. At intermediate densities, stochastically oriented crystalline nuclei are observed. Specific atomic aggregates — stacks of five-membered rings in good tetrahedral configurations of spheres — are revealed in models having a substantial fraction of crystalline phase (η = 0.664). Such non-trivial structures can occur only in packings that are intermediate between amorphous and crystalline phases.     

HPLC Study of the Kinetics of Intramolecular Cyclization of Two New Phenyldiazene Molecules. Analytical Properties of the Resulting Liquid Crystals

A group of zeolites and a 3D nanoporous metal-organic material RPM-1 were tested as column packings for adsorption of isotactic polypropylene and linear polyethylene from dilute solutions. It was found that polyethylene is fully or partially retained from thermodynamically good solvents (1,1,2,2-tetrachloroethylene, 1,4-dimethylbenzene, diphenylether, 1,2-dichlorobenzene and 1,3-dichlorobenzene) at temperatures of 115 °C or 140 °C, when a specific type of zeolite with pore sizes 5–6 Å has been used as the column packing. Polypropylene was fully retained in another type of zeolite with pores of 7–12 Å, when diphenylether was used as the mobile phase. As far as known, this is the first system sorbent - mobile phase, where adsorption of polypropylene was observed.     

Numerical analysis of electroosmotic flow in dense regular and random arrays of impermeable, nonconducting spheres

We present a numerical scheme for analyzing steady-state isothermal electroosmotic flow (EOF) in three-dimensional random porous media, involving solution of the coupled Poisson, Nernst-Planck, and Navier-Stokes equations. While traditional finite-difference methods were used to resolve the Poisson-Nernst-Planck problem, the (electro)hydrodynamics has been addressed with high efficiency using the lattice-Boltzmann method. The developed model allows simulation of electrokinetic transport under most general conditions, including arbitrary value and distribution of electrokinetic potential at the solid-liquid interface, electrolyte composition, and pore space morphology. The approach provides quantitative information on a spatial distribution of simulated velocities. This feature was utilized to characterize EOF fields in regular and random, confined and bulk packings of hard (i.e., impermeable, nonconducting) spheres. Important aspects of pore space morphology (sphere size distribution), surface heterogeneity (mismatch in electrokinetic potentials at confining wall and sphere surface), and fluid phase properties (electrical double layer thickness) were investigated with respect to their influence on the EOF dynamics over microscopic and macroscopic spatial domains. Most important is the observation of a generally nonuniform pore-level EOF velocity profile in the sphere packings (even in the thin double layer limit) which is caused by pore space morphology and which is in contrast to the pluglike velocity distribution in a single, straight capillary under the same conditions.     

Chromatographic performance of monolithic and particulate stationary phases. Hydrodynamics and adsorption capacity

Monolithic chromatographic support structures offer, as compared to the conventional particulate materials, a unique combination of high bed permeability, optimized solute transport to and from the active surface sites and a high loading capacity by the introduction of hierarchical order in the interconnected pore network and the possibility to independently manipulate the contributing sets of pores. While basic principles governing flow resistance, axial dispersion and adsorption capacity are remaining identical, and a similarity to particulate systems can be well recognized on that basis, a direct comparison of sphere geometry with monolithic structures is less obvious due, not least, to the complex shape of theskeleton domain. We present here a simple, widely applicable, phenomenological approach for treating single-phase incompressible flow through structures having a continuous, rigid solid phase. It relies on the determination of equivalent particle (sphere) dimensions which characterize the corresponding behaviour in a particulate, i.e. discontinuous bed. Equivalence is then obtained by dimensionless scaling of macroscopic fluid dynamical behaviour, hydraulic permeability and hydrodynamic dispersion in both types of materials, without needing a direct geometrical translation of their constituent units. Differences in adsorption capacity between particulate and monolithic stationary phases show that the silica-based monoliths with a bimodal pore size distribution provide, due to the high total porosity of the material of more than 90%, comparable maximum loading capacities with respect to random-close packings of completely porous spheres.     

Geometrical cluster ensemble analysis of random sphere packings

We introduce a geometric analysis of random sphere packings based on the ensemble averaging of hard-sphere clusters generated via local rules including a nonoverlap constraint for hard spheres. Our cluster ensemble analysis matches well with computer simulations and experimental data on random hard-sphere packing with respect to volume fractions and radial distribution functions. To model loose as well as dense sphere packings various ensemble averages are investigated, obtained by varying the generation rules for clusters. Essential findings are a lower bound on volume fraction for random loose packing that is surprisingly close to the freezing volume fraction for hard spheres and, for random close packing, the observation of an unexpected split peak in the distribution of volume fractions for the local configurations. Our ensemble analysis highlights the importance of collective and global effects in random sphere packings by comparing clusters generated via local rules to random sphere packings and clusters that include collective effects.     

Preparation and evaluation of a well-ordered mesoporous nickel-molybdenum/silica opal hydrodesulfurization model catalyst

A silica-supported hydrodesulfurization (HDS) model catalyst with well-ordered pore structure was prepared by depositing Ni and Mo on the surface of silica opal. Using the voids of ordered packing of monodisperse silica microspheres, the pores of the model catalyst are wholly open-through and uniformly distributed. The ordered pore structure and regular smooth surface of the model catalyst make the surface states of metal oxides readily observable. As a result, the metal oxides were well dispersed on the silica, and the model catalyst exhibited a high activity in HDS of dibenzothiophene.     

From random sphere packings to regular pillar arrays: effect of the macroscopic confinement on hydrodynamic dispersion

Flow and mass transport in bulk and confined chromatographic supports comprising random packings of solid, spherical particles and hexagonal arrays of solid cylinders (regular pillar arrays) are studied over a wide flow velocity range by a numerical analysis scheme, which includes packing generation by a modified Jodrey-Tory algorithm, three-dimensional flow field calculations by the lattice-Boltzmann method, and modeling of advective-diffusive mass transport by a random-walk particle-tracking technique. We demonstrate the impact of the confinement and its cross-sectional geometry (circular, quadratic, semicircular) on transient and asymptotic transverse and longitudinal dispersion in random sphere packings, and also address the influence of protocol-dependent packing disorder and the particle-aspect ratio. Plate height curves are analyzed with the Giddings equation to quantify the transcolumn contribution to eddy dispersion. Confined packings are compared with confined arrays under the condition of identical bed porosity, conduit cross-sectional area, and laterally fully equilibrated geometrical wall and corner effects on dispersion. Fluid dispersion in a regular pillar array is stronger affected by the macroscopic confinement and does not resemble eddy dispersion in random sphere packings, because the regular microstructure cannot function as a mechanical mixer like the random morphology. Giddings' coupling theory fails to preserve the nature of transverse dispersion behind the arrays' plate height curves, which approach a linear velocity-dependence as transverse dispersion becomes velocity-independent. Upon confinement this pseudo-diffusive behavior can outweigh the performance advantage of the regular over the random morphology.     

Porous Cu-Cd mixed-metal-organic frameworks constructed from Cu(Pyac)2 [Bis[3-(4-pyridyl)pentane-2,4-dionato]copper(II)

Porous Cu-Cd mixed-metal-organic frameworks [[Cd(NO(3))(2)](2)[(Cu(Pyac)(2)](3)] (M'MOF 1) and [[CdCl(2)][Cu(Pyac)(2)](2)] (M'MOF2) [Cu(Pyac)(2) = bis[3-(4-pyridyl)pentane-2,4-dionato]copper(II)] have been synthesized by the reaction of Cu(Pyac)(2) with Cd(NO(3))(2) and CdCl(2). They are noninterpenetrating 1D ladder and 2D square-grid frameworks, constructed from Cu(Pyac)(2) building blocks with T-shaped Cd(NO(3))(2) nodes and square-planar CdCl(2) nodes, respectively. The 1D ladders and 2D square grids are stacked in ABCABC... and ABCDEF... packings, leading to 2D interconnected channels of ca. 5.7 x 10.2 and 4.1 x 9.8 A in 1 and 1D channels of ca. 8.0 x 8.2 A in 2, respectively. The copper sites in these two M'MOFs are coordinated by solvent molecules and exposed to the pores.     

新型离子交换硅胶键合相的制备及评价

二甲基氯硅烷与硅胶表面反应,形成牢固的ＳｉＨ键之后,连接上活泼的中间体——烯丙基缩甘油醚作为柔软的分子臂,最后接上二乙基氨基,由此制得了新型的离子交换硅胶键合相。经漫反射红外光谱、元素分析和高效液相色谱法对键合相进行了鉴定和评价。结果表明：键合反应按预定路线进行,键合相具有较好的色谱性能。此种方法可有效地运用于无孔硅胶填料的制备。     

Microbubble generation in a co-flow device operated in a new regime

A new regime of operation of PDMS-based flow-focusing microfluidic devices is presented. We show that monodisperse microbubbles with diameters below one-tenth of the channel width (here w = 50 μm) can be produced in low viscosity liquids thanks to a strong pressure gradient in the entrance region of the channel. In this new regime bubbles are generated at the tip of a long and stable gas ligament whose diameter, which can be varied by tuning appropriately the gas and liquid flow rates, is substantially smaller than the channel width. Through this procedure the volume of the bubbles formed at the tip of the gas ligament can be varied by more than two orders of magnitude. The experimental results for the bubble diameter d(b) as function of the control parameters are accounted for by a scaling theory, which predicts d(b)/w ∝ (μ(g)/μ(l))(1/12)(Q(g)/Q(l))(5/12), where μ(g) and μ(l) indicate, respectively, the gas and liquid viscosities and Q(g) and Q(l) are the gas and liquid flow rates. As a particularly important application of our results we produce monodisperse bubbles with the appropriate diameter for therapeutic applications (d(b) ? 5 μm) and a production rate exceeding 10(5) Hz.     

Atypical silica-based column packings for high-performance liquid chromatography

Column packings widely used for high-performance liquid chromatography (HPLC) mostly are based on porous silica microspheres with certain pore sizes and pore size distributions. Such materials have the most desirable compromise of properties that provide for effective and reproducible separations over a wide range of operating conditions. To provide desired separation characteristics, several manufacturers specially synthesize the silica particles for these packings. While such column packing materials have general utility for a wide range of needs, special silica-based particles have been synthesized with different physical conformations for special separation goals. This presentation describes some atypical types of silica-based particles with unique separation properties that enlarge the capabilities of HPLC methods.     

Triple framework interpenetration and immobilization of open metal sites within a microporous mixed metal-organic framework for highly selective gas adsorption

A three-dimensional triply interpenetrated mixed metal-organic framework, Zn(2)(BBA)(2)(CuPyen)·G(x) (M'MOF-20; BBA = biphenyl-4,4'-dicarboxylate; G = guest solvent molecules), of primitive cubic net was obtained through the solvothermal reaction of Zn(NO(3))(2), biphenyl-4,4'-dicarboxylic acid, and the salen precursor Cu(PyenH(2))(NO(3))(2) by a metallo-ligand approach. The triple framework interpenetration has stabilized the framework in which the activated M'MOF-20a displays type-I N(2) gas sorption behavior with a Langmuir surface area of 62 m(2) g(-1). The narrow pores of about 3.9 ? and the open metal sites on the pore surfaces within M'MOF-20a collaboratively induce its highly selective C(2)H(2)/CH(4) and CO(2)/CH(4) gas separation at ambient temperature.     

Influence of the packing heterogeneity on the performance of liquid chromatography supports

We report on a series of plate height and flow resistance data obtained via computational fluid dynamics simulations in a simplified two-dimensional (2D) mimic of real packed bed and monolithic columns. By varying the external porosity (0.4 < epsilon < 0.8) and the degree of packing randomness, a good qualitative insight in the relationship between the packing porosity and heterogeneity and the general chromatographic performance parameters is obtained, unbiased by any differences in phase retention factor k', mobile phase diffusivity or viscosity or intra-skeleton porosity. The results provide a quantitative support for the use of domain size reduced plate heights as a means to compare the performance of chromatographic beds with a different porosity, as it was found that packings with a similar degree of packing heterogeneity yield very similar domain size reduced h(min)-values, nearly completely independent of the porosity. The study also clearly shows that the presence of preferential flow paths (inevitably accompanied by the presence of more clustered regions) leads to a decrease of the flow resistance, but also leads to a strong increase of the band broadening if supports with the same porosity epsilon and the same radial width are compared. For the presently considered 2D system, the flow resistance reduction is too small to overcome the corresponding strong increase in band broadening, such that the presence of preferential flow paths always leads to an overall increase of the separation impedance.     

Study of SPG membrane emulsification processes for the preparation of monodisperse core-shell microcapsules

Experimental investigations on the Shirasu-porous-glass (SPG)-membrane emulsification processes for preparing monodisperse core-shell microcapsules with porous membranes were carried out systematically. The results showed that, to get monodisperse oil-in-water (O/W) emulsions by SPG membrane emulsification, it was more important to choose an anionic surfactant than to consider hydrophile-lipophile balance (HLB) matching. Increasing the viscosity of either the disperse phase or the continuous phase or decreasing the solubility of the disperse phase in the continuous phase could improve both the monodispersity and the stability of emulsions. With increasing monomer concentration inside the disperse phase, the monodispersity of emulsions became slightly worse and the mean diameter of emulsions gradually became smaller. Monodisperse monomer-containing emulsions were obtained when the SPG membrane pore size was larger than 1.0 micro m, and from these emulsions satisfactory monodisperse core-shell microcapsules with a porous membrane were prepared. On the other hand, when the SPG membrane pore size was smaller than 1.0 mciro m, no monodisperse emulsions were obtained because of the formation and chokage of solid monomer crystals in the pores or at the end of the pores of the SPG membrane. This was due to the remarkable solvation and diffusion of the solvent in water. With increasing the emulsification time the average emulsion diameter generally decreased, and the monodispersity of the emulsions gradually became worse.     

Structural characteristics of close packings of hard spheres. Critical densities

For packings of similar hard spheres, there are several characteristic values of density. First, this is the maximal possible degree of space filling by spheres η = 0.74, realized for the crystalline packing of spheres. Another known value, η = 0.64, is the limiting (critical) value for disordered packings. We also indicate two more characteristic values of density: η = 0.60 and η = 0.66, in the vicinity of which qualitative changes in structure can occur. Computer models of the packings of hard spheres are investigated in the range of densities 0.52 < η < 0.72. Each packing consisted of 10,000 spheres in a cube with periodic boundary conditions. The structural characteristics were investigated using Delaunay simplices, defining the arrangement of the nearest four atoms. Simplices that are close to a regular tetrahedron or quartoctahedron (quarter of an octahedron) are considered. These forms are typical for the densest crystal structures. Variation of the fraction and ratio of these simplices is studied as a function of the packing density. According to the results, the threshold value, η = 0.60, corresponds to the density after which correlation of the disordered arrangement of spheres increases considerably. When η = 0.64, the structural organization changes more radically; high density demands the emergence of local crystal nuclei. The density η = 0.66 is the limiting density at which the crystalline nuclei can exist as independently distributed regions. Closer packings can only occur if a global crystal structure arises in them.     

Pair diffusion, hydrodynamic interactions, and available volume in dense fluids

We calculate the pair diffusion coefficient D(r) as a function of the distance r between two hard sphere particles in a dense monodisperse fluid. The distance-dependent pair diffusion coefficient describes the hydrodynamic interactions between particles in a fluid that are central to theories of polymer and colloid dynamics. We determine D(r) from the propagators (Green's functions) of particle pairs obtained from molecular dynamics simulations. At distances exceeding ~3 molecular diameters, the calculated pair diffusion coefficients are in excellent agreement with predictions from exact macroscopic hydrodynamic theory for large Brownian particles suspended in a solvent bath, as well as the Oseen approximation. However, the asymptotic 1/r distance dependence of D(r) associated with hydrodynamic effects emerges only after the pair distance dynamics has been followed for relatively long times, indicating non-negligible memory effects in the pair diffusion at short times. Deviations of the calculated D(r) from the hydrodynamic models at short distances r reflect the underlying many-body fluid structure, and are found to be correlated to differences in the local available volume. The procedure used here to determine the pair diffusion coefficients can also be used for single-particle diffusion in confinement with spherical symmetry.