Accurate relations between pore size and the pressure of capillary condensation and the evaporation of nitrogen in cylindrical pores

To examine the theoretical and semiempirical relations between pore size and the pressure of capillary condensation or evaporation proposed so far, we constructed an accurate relation between the pore radius and the capillary condensation and evaporation pressure of nitrogen at 77 K for the cylindrical pores of the ordered mesoporous MCM-41 and SBA-15 silicas. Here, the pore size was determined from a comparison between the experimental and calculated X-ray diffraction patterns due to X-ray structural modeling recently developed. Among the many theoretical relations that differ from each other in the degree of theoretical improvements, a macroscopic thermodynamic approach based on Broekhoff-de Boer equations was found to be in fair agreement with the experimental relation obtained in the present study.     

Distribution of the active component among pores of different size (microdistribution)

The role of active component distribution among the pores of different size in supported catalysts has been examined. The influence of microdistribution on catalyst pellet activity and stability were studied. It was shown that the microdistribution parameter does not affect the pellet effectiveness factor in the case of gas-phase reactions. High catalyst stability can be achieved when the fraction of micropores does not exceed 30–40%, otherwise the deactivation rate constants in small and large pores differ less than 5 times.     

A new method for the simultaneous determination of the size and shape of pores: the thermoporometry

A thermodynamic study of the liquid—solid phase transformations in porous materials provides the relationships between the size of the pores in which solidification takes place and the temperature of the triple point of the divided liquid, on the one hand, and between this temperature and the apparent solidification energy on the other hand.The experimental study of the phase transformations, carried out by means of a microcalorimeter, gives the values of the parameters necessary to calculate the free solid = liquid interphase extension energy γ_ls at different temperatures. A formula γ_ls  f(T) is given for water and benzene. Once this factor is known, it is possible to study the numerical relationship between pore-radius and freezing energy at the equilibrium temperature.By using these relations together with the solidification thermogram (the recording of the power evolved by the solidification of a capillary condensate during a linear decrease of temperature) the authors have been able to determine pore distribution curves. An emphasis is put on the comparison between this method, thermoporometry, and the B.J.H. method.Last of all the comparison of the experimental data for solidification and melting provide information concerning pore shape by means of the evaluation of a thermodynamic shape factor or by a method of simulation of porous material.     

Polymolecular adsorption and capillary condensation in narrow slit pores

Capillary condensation and polymolecular adsorption in narrow slits has been calculated, where the fields of surface forces overlap one another. The calculations were carried out on the basis of macroscopic theory of dispersion forces and the isotherms of lone adsorption layers at the free surface. It has been shown that under the effect of mutual attraction through a gap, polymolecular adsorption films lose their stability long before their thickness has approached the half-width of a flat slit. This results in hysteresis of the capillary condensation in an ensemble of plane-parallel slits.

In the case of systems having strong adsorbate-adsorbate interaction, there has been detected the existence of the lower limit of sizes of slit pores, wherein the capillary meniscus can coexist with adsorption films. With a slit width smaller than the critical one, the meniscus is likely to form a finite contact angle with “dry” surfaces of a slit. Thus an explanation has been given of the lower limit of the capillary condensation in an ensemble of flat-surface, slit pores. In the case of strong adsorbate-adsorbent interaction, the coexistence of meniscus with adsorption films within the scope of the approach used is possible in slits of any width.

The value of corrections for the surface forces effect to be entered in the calculations of slit pores dimensions has been analyzed on the basis of the capillary condensation data obtained.

In wedge-shaped slits there also exists, besides lower limit the upper limit of capillary hysteresis.     

Critical temperature of capillary condensation in narrow cylindrical pores

The dependence of the critical temperature of capillary condensation of an adsorbate in cylindrical pores on the diameter of pores is investigated. The calculation is carried out in the quasi-chemical approximation with a calibration function providing the agreement of results for small pores with exact values obtained by the fragment method. The contribution of the size effect to the calibration function as a function of the diameter of pores is considered in terms of the concept of quasi-one-dimensional behavior of the adsorbate in narrow pores. Various adsorbate-adsorbate potentials are considered.     

Three-phase capillary entry conditions in pores of noncircular cross-section

In this work we challenge the assumption that the capillary entry pressures for displacements in three-phase flow are the same as those in two-phase flow. Using an energy balance, as derived by R.P. Mayer and R.A. Stowe (J. Colloid Interface Sci. 20 (1965) 893-911) and H.M. Princen (J. Colloid Interface Sci. 30 (1969) 69-75; 30 (1969) 359-371; 34 (1970) 171-184) for two-phase flow, we derive a general formula for determination of the capillary entry pressures for piston-like displacement of two bulk phases in a pore where a third phase may also be present. The method applies to capillaries of angular cross-section and uniform but arbitrary wettability. To use this method we have determined all possible underlying phase occupancies in cross-sections on either side of the main terminal meniscus, in particular the presence of corner arc menisci (AMs). Indeed, the capillary entry pressures for piston-like displacements depend on the pressure in the remaining third phase if the cross-sectional fluid configurations contain this phase. This dependence only vanishes when layers of the intermediate-wetting phase completely separate the wetting and the non-wetting phases. The complexity of the corresponding equations and the quantitative effects are studied using two different geometries, the equilateral triangle and the rhombus. The main difference is that the latter geometry has unequal corners, which may carry different AMs. We have carried out a limited sensitivity study with respect to the effect of wettability, the spreading coefficient of the intermediate-wetting phase, and the aspect ratio of the principal radii of the rhombus.     

Studying the size/shape separation and optical properties of silver nanoparticles by capillary electrophoresis

This paper describes the feasibility of employing capillary electrophoresis (CE) to separate silver particles in nanometer regimes. We have found that the addition of an anionic surfactant, sodium dodecyl sulphate (SDS), to the running electrolyte prevents coalescence of the silver particles during the process, which improves the separation performance; the concentration of SDS required for optimal silver nanoparticle separation is ca. 20 mM. By monitoring the electropherograms using a diode-array detection (DAD) system, we have also investigated the separation of suspended silver nanorods with respect to their shapes. Our results demonstrate that the combination of CE and DAD is a powerful one for the separation and characterization of various silver nanoparticles.     

Rate of capillary rise in porous media with nonuniform pores

An equation for the rate of capillary rise in porous media with nonuniform pores has been derived on the basis of a three-dimensional network model of pore structure, consisting of a repeating capillary element with step changes in its diameter. The measured rates of capillary rise of water in a number of sandstone samples have been accurately predicted by the model. The apparent capillary diameter for the rate of the capillary rise has been found to be several orders of magnitude smaller than the pore diameter corresponding to the peak of the mercury intrusion porosimetry curve. The permeability of the sandstone samples has been found to be approximately directly proportional to the apparent diameter of the rate of capillary rise. This approximate proportionality has been shown to follow from the capillary network model of the pore structure used in this work.     

Hemimicelle shape and size

Based on the assumption of spherical hemimicelle with a hydrophobic core of diameter of maximum hydrocarbon chain length of surfactant, the aggregation numbers of hemimicelles have been calculated for several values ofn, the carbon atoms of surfactant alkyl chain. The results are in reasonable good agreement with the hemimicelle aggregation number from experimental data for several corresponding systems. The other possibilities of the hemimicelle shape which allow to incorporate a larger number of hydrocarbon chains in a hemimicelle have also been discussed.On leave from Department of Chemistry, Peking University, Beijing, China     

Sorting cells by size, shape and deformability

While size has been widely used as a parameter in cellular separations, in this communication we show how shape and deformability, a mainly untapped source of specificity in preparative and analytical microfluidic devices can be measured and used to separate cells.     

Zinc oxide colloids with controlled size, shape, and structure

Highly dispersed uniform ZnO particles of different sizes and shapes were prepared by slowly adding zinc salt and sodium hydroxide solutions in parallel into aqueous solutions of Arabic gum. Except for the very early stages, the precipitated solids consisted of a well-defined zinc oxide phase. Depending on the experimental conditions, the size of the final polycrystalline particles formed by the aggregation of nanosize entities varied from 100 to 300 nm. The reaction temperature affected both the size of the nanosize precursors and their arrangement in the final particles. At ambient temperature the primary nanoparticles, approximately 10 nm in size, formed spherical aggregates, while at 600 degrees C they were much larger (44 nm) and combined to form rather uniform hexagonal ZnO prisms. The aspect ratio and the internal structure of the latter could be altered by changing the nature of the zinc salt, the addition rate, and the initial concentration of the reactants. Based on the findings of the study a two-stage mechanism for the formation of uniform polycrystalline particles with well-defined geometric shapes is proposed.     

Unusual mechanism of capillary condensation in pores modified with chains forming pillars

Density functional approach is applied to study the phase behavior of Lennard-Jones(12,6) fluid in pillared slit-like pores. Our focus is in the evaluation of phase transitions in fluid adsorbed in the pore of a fixed width. If the length of pillars is sufficiently large, we observe additional phase transitions of the first and second order due to the symmetry breaking of the distribution of chain segments and fluid species with respect to the slit-like pore center. Re-entrant symmetry changes and additional critical, critical end points and tricritical points then are observed. The scenario of phase changes is sensitive to the energy of fluid-solid interaction, the amount, and the length of the pillars. Quantitative trends and qualitative changes of the phase diagrams topology are examined depending on the values of these parameters.     

Imparting size, shape, and composition control of materials for nanomedicine

This tutorial review presents an overview of strategies for the synthesis and fabrication of organic nanomaterials, specifically those with potential for use in medical applications. Examples include liposomes, micelles, polymer-drug conjugates and dendrimers. Methods of driving shape via"bottom-up" synthetic approaches and thermodynamics and kinetics are discussed. Furthermore, methods of driving shape via"top-down" physical and engineering techniques are also explored. Finally, a novel method (referred to as PRINT) used to produce nanoparticles that are shape-specific, can contain any cargo, and can be easily modified is examined along with its potential future role in nanomedicine.     

Tactoids of plate-like particles: size, shape, and director field

We studied, by means of polarized light microscopy, the shape and director field of nematic tactoids as a function of their size in dispersions of colloidal gibbsite platelets in polar and apolar solvents. Because of the homeotropic anchoring of the platelets to the interface, we found large tactoids to be spherical with a radial director field, whereas small tactoids turn out to have an oblate shape and a homogeneous director field, in accordance with theoretical predictions. The transition from a radial to a homogeneous director field seems to proceed via two different routes depending in our case on the solvent. In one route, the what presumably is a hedgehog point defect in the center of the tactoid transforms into a ring defect with a radius that presumably goes to infinity with decreasing drop size. In the other route, the hedgehog defect is displaced from the center to the edge of the tactoid, where it becomes virtual again going to infinity with decreasing drop size. Furthermore, quantitative analysis of the tactoid properties provides us with useful information on the ratio of the splay elastic constant and the anchoring strength and the ratio of the anchoring strength and the surface tension.     

Self-assembly, structural, and retrostructural analysis of dendritic dipeptide pores undergoing reversible circular to elliptical shape change

The synthesis of dendritic dipeptides (4-3,4-3,5-4)12G2-CH(2)-Boc-L-Tyr-L-Ala-OMe and (4-3, 4-3,5-4)12G2-CH(2)-Boc-D-Tyr-D-Ala-OMe is described. These dendritic dipeptides self-assemble into porous elliptical and circular columns that in turn self-organize into centered rectangular columnar and hexagonal columnar periodic arrays. The transition from porous elliptical to porous circular columns is mediated in a reversible or irreversible way by the thermal history of the sample. A method to determine the dimensions of hollow elliptical and circular columns by the reconstruction of the small-angle powder X-ray diffractograms of the centered rectangular or hexagonal columnar lattices was elaborated. This technique together with wide-angle X-ray experiments performed on aligned fibers provided access to the structural and retrostructural analysis of elliptical supramolecular pores. This procedure is general and can be adapted for the determination of the dimensions of pores of any columnar shape.     

Electrochemistry of capillary systems with narrow pores III. Electrical conductivity

The extension of the Teorell–Meyer–Sievers theory of the dialysis potential to a general theory of capillary systems with narrow pores outlined in Part I of this series of publications has been applied to electroosmotic phenomena in Part II. In this Part, the electrical conductivity, including the electrical convection conductivity, will be treated in terms of the new theory. The corresponding equations already referred to in Part I are derived. In addition, results of measurements of the electrical conductivity of collodion membranes with graded porosity and graded electrochemical activity in aqueous KCl solutions of different concentrations are reported. They are used to test the new theory. It will be shown that it is possible to determine the fixed ion concentration A of the membranes by using electrical conductivity data. The theory predicts that the value of A should be identical with the ‘selectivity constant' of the Meyer–Sievers theory of the dialysis potential. This prediction will be checked in Part IV of this series of contributions.     

Electrochemistry of capillary systems with narrow pores. I. Overview

In capillary systems with narrow pores the Helmholtz electrochemical double layer located at the pore wall extends over the entire cross section of the pores. It loses its character as the “charge on the wall”. It will be shown that not only the electrokinetic phenomena but also the electrical conductivity and the dialysis potential of membranes with narrow pores can be understood from the same point of view, namely: the electrolyte solution in the pores of a membrane with narrow pores is considered to be an approximately homogeneous solution in contact with immobilised charges located at the pore wall. In this case the electrochemical equations contain the fixed ion concentration as a parameter instead of the ζ potential. This makes it possible to describe quantitatively to a good approximation data on the electroosmosis, the electrical conductivity, the streaming potential and the dialysis potential taken from the literature, as well as results of our own measurements, by using a single membrane constant.     

Electrochemistry of capillary systems with narrow pores. II. Electroosmosis

Manegold and Solf have reported systematic deviations of the electroosmotic properties of collodion membranes with narrow pores from predictions based on the Helmholtz–Smoluchowski model. To interpret the electroosmotic data quantitatively it is necessary to replace the assumption of the Helmholtz–Smoluchowski model that the thickness of the electric double layer is small compared with the pore radius by a new assumption. We have assumed that the counter ions are distributed homogeneously in the pore fluid. In Part I of this series of contributions, equations have been given describing the electroosmotic properties of a membrane with narrow pores based on the new assumption. These equations are derived here in detail and are applied to an analysis of the experimental data given by Manegold and Solf.     

Measuring location, size, distribution, and loading of NiO crystallites in individual SBA-15 pores by electron tomography

By the combination of electron tomography with image segmentation, the properties of 299 NiO crystallites contained in 6 SBA-15 pores were studied. A statistical analysis of the particle size showed that crystallites between 2 and 6 nm were present with a distribution maximum at 3 and 4 nm, for the number-weighted and volume-weighted curves, respectively. Interparticle distances between nearest neighbors were 1-3 nm with very few isolated crystallites. In the examined pores, a local loading twice the applied average of 24 wt % NiO was found. This suggests that a very high local loading combined with a high dispersion is achievable.