The dynamic behavior of a stratified column bed packed with porous adsorbent particles having partially fractal structures and a nonuniform ligand density distribution

The dynamic behavior of adsorption in a single column and in stratified column beds packed with porous adsorbent particles having partially fractal structures is studied when all columns have the same total length and the spatial ligand density distribution in the porous microspheres from which the porous adsorbent particles are made, is either uniform or nonuniform and such that the concentration of the immobilized ligands (active sites) increases monotonically from the center of the microspheres to their outer surface. The total number of immobilized ligands in the porous adsorbent particles has the same value whether the spatial ligand density distribution is uniform or nonuniform. The results in this study clearly show that for a given value of the superficial velocity of the flowing fluid stream in the column (for a given value of throughput) the breakthrough time is significantly increased when the radius of the microspheres is decreased, the total number of sections of the stratified column bed is increased, and the spatial ligand density distribution employed in the microspheres is nonuniform. Furthermore, when the superficial velocity of the flowing fluid stream in the column is increased (throughput is increased) the effect that (i) the reduction in the radius of the microspheres and (ii) the increase in the number of sections of the stratified column bed have on providing robust and effective dynamic adsorptive capacity and smaller reductions on the breakthrough time is substantially larger than that realized through the use of the nonuniform ligand density distribution. Similar trends are also observed in the dynamic behavior of adsorption in the systems studied here when the value of the concentration of the adsorbate in the flowing fluid stream entering the column (inlet concentration) has such a high magnitude that the value of the equilibrium concentration of the adsorbate in the adsorbed phase determined from the equilibrium Langmuir isotherm that would correspond to the inlet concentration of the adsorbate in the flowing fluid stream is, for all practical purposes, at its saturation limit.     

The interplay of diffusional and electrophoretic transport mechanisms of charged solutes in the liquid film surrounding charged nonporous adsorbent particles employed in finite bath adsorption systems

A model that describes the diffusive and electrophoretic mass transport of the cation and anion species of a buffer electrolyte and of a charged adsorbate in the liquid film surrounding nonporous adsorbent particles in a finite bath adsorption system, in which adsorption of the charged adsorbate onto the charged surface of the nonporous particles occurs, is constructed and solved. The dynamic behavior of the mechanisms of this model explicitly demonstrates (a) the interplay between the diffusive and electrophoretic molar fluxes of the charged adsorbate and of the species of the buffer electrolyte in the liquid film surrounding the nonporous adsorbent particles, (b) the significant effect that the functioning of the electrical double layer has on the transport of the charged species and on the adsorption of the charged adsorbate, and (c) the substantial effect that the dynamic behavior of the surface charge density has on the functioning of the electrical double layer. It is found that at equilibrium, the value of the concentration of the charged adsorbate in the fluid layer adjacent to the surface of the adsorbent particles is significantly greater than the value of the concentration of the adsorbate in the finite bath, while, of course, the net molar flux of the charged adsorbate in the liquid film is equal to zero at equilibrium. This result is very different than that obtained from the conventional model that is currently used to describe the transport of a charged adsorbate in the liquid film for systems involving the adsorption of a charged adsorbate onto the charged surface of nonporous adsorbent particles; the conventional model (i) does not consider the existence of an electrical double layer, (ii) assumes that the transport of the charged adsorbate occurs only by diffusion in the liquid film, and (iii) causes at equilibrium the value of the charged adsorbate in the liquid layer adjacent to the surface of the particles to become equal to the value of the concentration of the charged adsorbate in the liquid of the finite bath. Furthermore, it was found that a maximum can occur in the dynamic behavior of the concentration of the adsorbate in the adsorbed phase when the value of the free molecular diffusion coefficient of the adsorbate is relatively large, because the increased magnitude of the synergistic interplay between the diffusive and electrophoretic molar fluxes of the adsorbate in the liquid film allows the adsorbate to accumulate (to be entrapped) in the liquid layer adjacent to the surface of the adsorbent particles faster than the concentrations of the electrolyte species, whose net molar fluxes are significantly hindered due to their opposing diffusive and electrophoretic molar fluxes, can adjust to account for the change in the surface charge density of the particles that arises from the adsorption of the charged adsorbate. The results presented in this work also have significant implications in finite bath adsorption systems involving the adsorption of a charged adsorbate onto the surface of the pores of charged porous adsorbent particles, because the diffusion and the electrophoretic migration of the charged solutes (cations, anions, and charged adsorbate) in the pores of the adsorbent particles will depend on the dynamic concentration profiles of the charged solutes in the liquid film surrounding the charged porous adsorbent particles. The results of the present work are also used to illustrate how the functioning of the electrical double layer could contribute to the development of inner radial humps (concentration rings) in the concentration of the adsorbate in the adsorbed phase of charged porous adsorbent particles.     

Adsorption of proteins on mesoporous carbon adsorbents

A study of the sorption of bull serum albumin (BSA) on carbon adsorbents with different porous structures has shown that, for adsorbents with globular structures, sorption depends on the size of the adsorbent particles. An assumption has been made concerning the nonequilibrium nature of BSA sorption on mesoporous adsorbents associated with irreversible adsorption of the protein and the nonuniform distribution of the adsorbed protein within the adsorbent particles.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 8, pp. 1737–1740, August, 1991.     

Analysis of mass transport models for protein adsorption to cation exchanger by visualization with confocal laser scanning microscopy

The mass transfer of bovine serum albumin (BSA) to a cation exchanger, SP Sepharose FF, has been studied by finite batch adsorption experiments. The uptake curve was simulated with three mass transport models (i.e., effective pore diffusion model, surface diffusion model and Maxwell-Stefan model) incorporating the particle size distribution of the adsorbent particles. All the three models can simulate the uptake curves reasonably well. However, how well these models could simulate the real concentration profile within the adsorbent particle cannot be verified by the fitness of the models to the uptake curve. Thus, confocal laser scanning microscopy (CLSM) was used to visualize protein uptake to the porous adsorbent particles during the batch experiments. Using a fluorescent dye-labeled bovine serum albumin (BSA) for the dynamic adsorption experiments, the radial concentration profiles of the labeled BSA molecules into individual adsorbent particles at different times were obtained from the CLSM images. The protein distribution profiles within various particle diameters at different time were compared with the radial protein distributions predicted from the models. It reveals that surface diffusion model describes the intraparticle protein concentration profiles better than the other two models.     

Molecular dynamics simulation studies of the conformation and lateral mobility of a charged adsorbate biomolecule: implications for estimating the critical value of the radius of a pore in porous media

The conformations, the values of the lateral transport coefficient of a charged biomolecule (desmopressin) in the adsorbed layer and in the liquid layers above the adsorbed layer, the potential energies of the interaction between the biomolecules located in different liquid layers with the charged solid surface and with the biomolecules in the adsorbed layer, the potential energies of the interaction between water molecules in the hydration layers surrounding the conformations of the biomolecules in different layers, as well as the structure and number of hydration layers between the different conformations of desmopressin, were determined by molecular dynamics simulation studies. The results show that the lateral mobility of the adsorbed desmopressin is approximately equal to zero and the value of the lateral transport coefficient of the biomolecule in the liquid layers located above the adsorbed layer increases as the distance of the liquid layer from the charged solid surface increases. But the values of the lateral transport coefficient of the biomolecule in the liquid layers above the adsorbed layer are lower in magnitude than the value of the transport coefficient of desmopressin along the direction normal to the charged solid surface in the liquid phase located above the vacant charged sites of the solid surface, and these differences in the values of the transport coefficients have important implications with respect to the replenishment of the biomolecules in the inner parts of a channel (pore), the overall rate of adsorption, and the form of the constitutive equations that would have to be used in macroscopic models to describe the mechanisms of mass transfer and adsorption in the pores of adsorbent media. Furthermore, a novel method is presented in this work that utilizes the information about the sizes of the conformations of the biomolecule in the adsorbed layer and in the liquid layers above the adsorbed layer along the direction that is normal to the charged solid surface, as well as the number and size of the hydration layers along the same direction, and could be used to estimate the value of the lower bound of the linear characteristic dimension of a pore (i.e., pore radius) in porous adsorbent media (e.g., porous adsorbent particles; skeletons of porous monoliths) in order to realize effective transport and overall adsorption rate.     

On the theory of polyelectrolyte adsorption : The effect on adsorption behavior of the electrostatic contribution to the adsorption free energy

A theory has been developed for the adsorption of polyelectrolytes on charged interfaces from an aqueous salt solution. This adsorption is determined by the electrical charge density of the polyelectrolyte, the adsorption energy, the salt concentration, the molecular weight, solubility, flexibility, and concentration of polymer. The theory relates these parameters to the properties of the adsorbed polymer layer, i.e., the amount of polymer adsorbed, the fraction of the adsorbent interface covered, the fraction of the segments actually adsorbed on the interface versus the fraction of the segments in the dangling loops, the final surface charge density, and the thickness of the adsorbed layer. As polyelectrolyte adsorption should resemble nonionic polymer adsorption at high ionic strength of the solution or low charge density on the polymer, this work is an extension of the nonionic polymer adsorption theory to polyelectrolyte adsorption. The following effects are taken into account: (a) the conformational change upon adsorption of a coil in solution into a sequence of adsorbed trains interconnected by loops dangling in solution; (b) the interactions of the adsorbed trains with the interface and with each other; (c) the interaction of the dangling loops with the solvent; (d) the change in surface charge density of the adsorbent due to adsorption of charged trains and the accompanying changes in the electrical double layer which contains “small” ions as well as charged loops; (e) the (induced) dipole interaction of the adsorbed trains with the charged adsorbent interface. The theory is worked out for low potentials (Debye—Hückel approximation); in Appendix B an outline of a more complete treatment is given. The predicted adsorption isotherms have the experimentally observed high-affinity character. A relation between the adsorption energy, the surface charge density on the adsorbent, the degree of dissociation of the polymer, and the salt concentration predicts the conditions under which no adsorption will occur. For adsorbent and polymer carrying the same type of charge (both positive or both negative) the adsorption is predicted to decrease with increased charge density on polymer or adsorbent and to increase with salt concentration. If adsorbent and polymer carry different type charges, the adsorption as a function of the degree of dissociation, α, goes through a maximum at a relatively low value of α and, depending on the adsorption energy, an increase in the salt concentration can then increase or decrease the adsorption. At finite polymer concentration in solution the number of adsorbed segments and the fraction of the interface covered practically do not change with an increase in polymer concentration, whereas the total number of polymer molecules adsorbed increases slightly, as does the average fraction of segments in loops. The experimental results for polyelectrolyte adsorption have been reviewed in general and, as far as data are available, the predictions of the theory seem to follow the experimentally observed trends quite closely, except for the thickness of the adsorbed layer. This thickness is systematically overestimated by the theory and two reasons for this are given. The theoretical model implies a not too low ionic strength of the solution. Extrapolation of results to solutions of very low ionic strength is not warranted.     

Effect of dextran layer on protein uptake to dextran-grafted adsorbents for ion-exchange and mixed-mode chromatography

In the current research, a series of dextran-grafted adsorbents were prepared using sulfopropyl and 4-(1H-imidazol-1-yl) aniline as chromatographic ligands for ion-exchange (IEC) and mixed-mode chromatography (MMC) to respectively investigate the influence of dextran layer on adsorption of γ-globulin. Experimental evidences of static adsorption on dextran-grafted IEC adsorbents showed that adsorption capacity of γ-globulin increased with dextran content. It could be attributed to the multilayer adsorption of charged protein in dextran layer and thus further induced a significant electrical potential gradient at the boundary of adsorbed area and its proximity, improving mass transfer in combination with concentration gradient. In contrast to IEC adsorbents, adsorption capacity and effective diffusivity of dextran-grafted MMC adsorbents did not change obviously with dextran grafting. It was considered that hydrophobic ligands immobilized onto dextran-grafted MMC adsorbents were stuck together at pH 8.0, resulting in the collapse of dextran layer. In concert with measured effective porosity for γ-globulin at pH 4.0, it was confirmed that dextran layer in MMC adsorbent was more complicated and influenced significantly by buffer pH. It was also manifested by protein adsorption at different pHs. Thus, it revealed the complexity in intraparticle mass transfer of the protein in dextran-grafted MMC adsorbent.     

Spectral luminescent study of orientation states of dye molecules adsorbed on a nonuniform surface

Brownian reorientation motion of molecules results in an equilibrium of orientation states of adsorbed molecules. The character of the orientation equilibrium depends on the total concentration of adsorbed molecules. Since optical properties of molecules are sensitive to the intermolecular interaction with an adsorbent, each orientation state has an individual luminescence spectrum. A change in the equilibrium results in complicated concentration and temperature dependences of the spectra of adsorbed molecules. These dependences have been experimentally observed for several dyes adsorbed on microporous silicate glass. Equilibrium constants and fractal dimensions of the spatial distribution of dye molecules in porous matrices have been determined.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 7, pp. 1284–1288, July, 1995.     

Construction by molecular dynamics modeling and simulations of the porous structures formed by dextran polymer chains attached on the surface of the pores of a base matrix: characterization of porous structures

Significant increases in the separation of bioactive molecules by using ion-exchange chromatography are realized by utilizing porous adsorbent particles in which the affinity group/ligand is linked to the base matrix of the porous particle via a polymeric extender. To study and understand the behavior of such systems, the M3B model is modified and used in molecular dynamics (MD) simulation studies to construct porous dextran layers on the surface of a base matrix, where the dextran polymer chains and the surface are covered by water. Two different porous polymer layers having 25 and 40 monomers per main polymer chain of dextran, respectively, are constructed, and their three-dimensional (3D) porous structures are characterized with respect to porosity, pore size distribution, and number of conducting pathways along the direction of net transport. It is found that the more desirable practical implications with respect to structural properties exhibited by the porous polymer layer having 40 monomers per main polymer chain, are mainly due to the higher flexibility of the polymer chains of this system, especially in the upper region of the porous structure. The characterization and analysis of the porous structures have suggested a useful definition for the physical meaning and implications of the pore connectivity of a real porous medium that is significantly different than the artificial physical meaning associated with the pore connectivity parameter employed in pore network models and whose physical limitations are discussed; furthermore, the methodology developed for the characterization of the three-dimensional structures of real porous media could be used to analyze the experimental data obtained from high-resolution noninvasive three-dimensional methods like high-resolution optical microscopy. The MD modeling and simulations methodology presented here could be used, considering that the type and size of affinity group/ligand as well as the size of the biomolecule to be adsorbed onto the affinity group/ligand are known, to construct different porous dextran layers by varying the length of the polymeric chain of dextran, the number of attachment points to the base matrix, the degree of side branching, and the number of main polymeric chains immobilized per unit surface area of base matrix. After the characterization of the porous structures of the different porous dextran layers is performed, then only a few promising structures would be selected for studying the immobilization of adsorption sites on the pore surfaces and the subsequent adsorption of the bioactive molecules onto the immobilized affinity groups/ligands.     

Effect of colloidal particle size on adsorbed monodisperse and bidisperse monolayers

Coating hydrogel films or microspheres by an adsorbed colloidal shell is one synthesis method for forming colloidosomes. The colloidal shell allows control of the release rate of encapsulated materials, as well as selective transport. Previous studies found that the packing density of self-assembled, adsorbed colloidal monolayers is independent of the colloidal particle size. In this paper we develop an equilibrium model that correlates the packing density of charged colloidal particles in an adsorbed shell to the particle dimensions in monodisperse and bidisperse systems. In systems where the molar concentration in solution is fixed, the increase in adsorption energy with increasing particle size leads to a monotonic increase in the monolayer packing density with particle radius. However, in systems where the mass fraction of the particles in the adsorbing solutions is fixed, increasing particle size also reduces the molar concentration of particles in solution, thereby reducing the probability of adsorption. The result is a nonmonotonic dependence of the packing density in the adsorbed layer on the particle radius. In bidisperse monolayers composed of two particle sizes, the packing density in the layer increases significantly with size asymmetry. These results may be utilized to design the properties of colloidal shells and coatings to achieve specific properties such as transport rate and selectivity.     

Direct visualisation of plasmid DNA in individual chromatography adsorbent particles by confocal scanning laser microscopy.

Confocal microscopy was used for the measurement of plasmid DNA adsorbed to individual adsorbent particles intended for anion-exchange and triple helix affinity chromatography. Plasmid DNA was visualized with the fluorescent dye YOYO-1, that forms a highly fluorescent complex with double stranded DNA. Confocal images were translated into fluorescence intensity profiles and the distribution of plasmid DNA in the particles was measured. The results that adsorption of plasmid DNA mainly takes place in an outer layer of the particles. The described procedure can also be advantageously used to demonstrate triple helix formation between plasmid DNA and immobilized oligonucleotides.     

Molecular dynamics and neutron scattering study of the dependence of polyelectrolyte dendrimer conformation on counterion behavior

Atomistic molecular dynamics (MD) simulations and contrast variation small angle neutron scattering (SANS) have been combined to investigate the Generation-5 polyelectrolyte polyamidoamine starburst dendrimer. This work reveals the dendrimer conformational dependence on counterion association at different levels of molecular charge. The accuracy of the simulations is verified through satisfactory comparison between modeled results, such as excess intra-dendrimer scattering length density distribution and hydration level, and their experimental counterparts. While the counterion distributions are not directly measureable with SANS, the spatial distribution of the counterions and their dendrimer association are extracted from the validated MD equilibrium trajectories. It is found that the conformation of the charged dendrimer is strongly dependent on the counterion association. Sensitivity of the distribution of counterions around charged amines to the counterion valency is qualitatively explained by adopting Langmuir adsorption theory. Moreover, via extending the concept of electrical double layer for compact charged colloids, we define an effective radius of a charged dendrimer including the spatial distribution of counterions in its vicinity. Within the same framework, the correlation between the strength of intra-dendrimer electrostatic repulsion and the counterion valency and dynamics is also addressed.     

Adsorption of acrylamide-based copolymers from aqueous solutions on clay granules

The equilibrium adsorption of three samples of high-molecular-mass acrylamide-sodium acrylate copolymers with a degree of ionization of 7?C34% from concentrated aqueous solutions on Khvalynsk clay granules with sizes of 1?C2 mm is investigated. The adsorption is studied under dynamic conditions in the absence of inorganic electrolytes at an initial concentration of copolymers in the solutions of 2 g/L. It is established that copolymer adsorption decreases with an increase in the content of the adsorbent. Copolymer with a low degree of ionization is adsorbed more intensely than the other samples are. Adsorption curves are described by the Freundlich equation. The parameters of this equation are determined as functions of the initial pH value and the content of charged groups. The influence of the degree of polymer chain ionization on the density of adsorption contacts of macromolecules with the adsorbent surface is discussed.     

Electrolyte exclusion from charged adsorbent: replica Ornstein-Zernike theory and simulations

Structural and thermodynamic properties of the restrictive primitive model +1:-1 electrolyte solution adsorbed in a disordered charged media were studied by means of the Grand Canonical Monte Carlo simulation and the replica Ornstein-Zernike theory. Disordered media (adsorbent, matrix) was represented by a distribution of negatively charged hard spheres frozen in a particular equilibrium distribution. The annealed counterions and co-ions were assumed to be distributed within the nanoporous adsorbent in thermodynamic equilibrium with an external reservoir of the same electrolyte. In accordance with the primitive model of electrolyte solutions, the solvent was treated as a dielectric continuum. The simulations were performed for a set of model parameters, varying the net charge of the matrix (i.e., concentrations of matrix ions) and of annealed electrolyte, in addition to the dielectric constant of the invading solution. The concentration of adsorbed electrolyte was found to be lower than the corresponding concentration of the equilibrium bulk solution. This electrolyte "exclusion" depends strongly on the dielectric constant of the invading solution, as also on concentrations of all components. The most important parameter is the net charge of the matrix. Interestingly, the electrolyte rejection decreases with increasing Bjerrum length for the range of parameters studied here. The latter finding can be ascribed to strong inter-ionic correlation in cases where the Bjerumm length is high enough. To a minor extent, the adsorption also depends on the spacial distribution of fixed charges in adsorbent material. The replica Ornstein-Zernike theory was modified to cater for this model and tested against the computer simulations. For the range of parameters explored in this work, the agreement between the two methods is very good. These calculations were also compared with the results of the classical Donnan theory for electrolyte exclusion.     

Composite cryogel with immobilized concanavalin A for affinity chromatography of glycoproteins

Composite cryogels containing porous adsorbent particles were prepared under cryogelation conditions. The composites with immobilized concanavalin A (Con A) were used for capturing glycoproteins. Adsorbent particles were introduced into the structure in order to improve the capacity and to facilitate the handling of the particles. The monolithic composite cryogels were produced from suspensions of polyvinyl alcohol particles and porous adsorbent particles and cross‐linked under acidic conditions at sub‐zero temperature. The cryogels were epoxy activated and Con A was immobilized as an affinity ligand. Binding and elution of horseradish peroxidase (HRP) was studied in batch experiment and in a chromatographic setup. Increasing adsorbent concentration in composite cryogels will increase ligand density, which therefore enhances the amount of bound HRP from 0.98 till 2.9 (milligram enzyme per milliliter of gel) in the chromatographic system. The material was evaluated in 10 cycles for binding and elution of HRP.     

Profiling protein-surface interactions of multicomponent suspensions via flow cytometry

This study presents the use of flow cytometry as a high-throughput quantifiable technique to study multicomponent adsorption interactions between proteins and surfaces. Flow cytometry offers the advantage of high-throughput analysis of multiple parameters on a very small sampling scale. This enables flow cytometry to distinguish between individual adsorbent particles and adsorbate components within a suspension. As a proof of concept study, the adsorption of three proteins--bovine serum albumin (BSA), bovine immunoglobulin gamma (IgG) and fibrinogen--onto five surface-modified organosilica microsphere surfaces was used as a model multicomponent system for analysis. By uniquely labeling each protein and solid support type with spectrally distinguishable fluorescent dyes, the adsorption process could be "multiplexed" allowing for simultaneous screening of multiple adsorbate (protein) and adsorbent (particle surface) interactions. Protein adsorption experiments quantified by flow cytometry were found to be comparable to single-component adsorption studies by solution depletion. Quantitative distribution of the simultaneous competitive adsorption of BSA and IgG indicated that, at concentrations below surface saturation, both proteins adsorbed onto the surface. However, at concentrations greater than surface saturation, BSA preferentially adsorbed. Multiplexed particle suspensions of optically encoded particles were modified to produce a positively and negatively charged surface, a grafted 3400 MW poly(ethylene glycol) layer, or a physisorbed BSA or IgG layer. It was observed that adsorption was rapid and irreversible on all of the surfaces, and preadsorbed protein layers were the most effective in preventing further protein adsorption.     

A qualitative approach to adsorption mechanism identification on microporous carbonaceous surfaces

The paper presents results of research on identification of localized and other adsorption mechanisms, on geometrically heterogeneous graphite-like carbonaceous surfaces. It attempts to get an insight into properties of individual adsorptive molecule movement near attractive adsorption sites, arising from adsorbent surface geometrical heterogeneities. In particular, a shape and volume of space occupied by the continuously moving molecule mass center are investigated. To this aim, kinematic equilibrium of the particle moving near a hypothetical microporous carbonaceous adsorbent wall is considered, and then compared with thermodynamic equilibrium. The proposed approach enables to examine effects of certain surface geometry on the shape and volume of space occupied by adsorbed particles, and so to outline temperature conditions for the localized adsorption mechanism predomination. Thus, it provides a cognitive basis to answer the question, what particular mechanism (localized or other—e.g. mobile) should be assumed for a class of adsorption systems in order to select the most appropriate mathematical adsorption model. Hence, it makes it possible for more reliable examination of real porous structures, based on adsorption measurements.     

Methane adsorption and diffusion in a model nanoporous carbon: an atomistic simulation study

A constricted slit model was introduced to improve, one step further, the performance of the simple slit model in prediction of the adsorption and diffusion behavior of simple molecules in the nanoporous carbons (NPCs). The grand canonical Monte Carlo (GCMC) and molecular dynamics (MD) simulations are performed to study the adsorption and diffusion behavior of methane within the constricted slit models. The models are called slit-1, 2, and 3 with constriction heights 5, 7, and 9 Å respectively. For comparison, we used the slit-0 name for the simple slit without constriction. Adsorption results show that at low pressures, the constriction increases the adsorbed amount irrespective of its height. Slit-2 with a constriction height as a molecular diameter has the greatest heat of adsorption and has highest loading at pressures up to 3,000 kPa. At high pressures, when all pores are filled, the adsorption trend is in line with the pore volumes of slits where slit-0 with higher pore volume is dominant. The density profiles in the models were calculated and examined. The spatial distribution of adsorbed methane molecules was examined by various radial distribution functions calculated by MD. Also, MD simulation results show that the diffusion coefficient of methane decreases in constricted slits. The calculated diffusion coefficients in slit-2 in the direction of the constriction are one order of magnitude smaller than the calculated one in the simple slit model but it is far from the experimental values in the NPCs.     

Adsorption of nanoparticles at the solid-liquid interface

The adsorption of differently charged nanoparticles at liquid-solid interfaces was investigated by in situ X-ray reflectivity measurements. The layer formation of positively charged maghemite (γ-Fe(2)O(3)) nanoparticles at the aqueous solution-SiO(2) interface was observed while negatively charged gold nanoparticles show no adsorption at this interface. Thus, the electrostatic interaction between the particles and the charged surface was determined as the driving force for the adsorption process. The data analysis shows that a logarithmic particle size distribution describes the density profile of the thin adsorbed maghemite layer. The size distribution in the nanoparticle solution determined by small angle X-ray scattering shows an average particle size which is similar to that found for the adsorbed film. The formed magehemite film exhibits a rather high stability.