Selective adsorption of metronidazole on conjugated microporous polymers

Conjugated microporous polymers (CMPs) have recently received extensive attention in oil/organic solvent-water separation field as a kind of ideal porous absorbents with tunable porosity, large surface areas, and super-hydrophobicity. However, reports on the application of CMPs in adsorption of hydrophilic contaminants from water are very few. In this work, we studied the adsorption of metronidazole (MNZ), a polar antibiotic, by two kinds of CMPs. The adsorption characteristics of MNZ by the CMPs, including adsorption kinetics, mechanism, and isotherm parameters were calculated. The adsorption kinetics of MNZ was well expressed by the pseudo-second-order model, and the adsorption process was found to be mainly controlled by film diffusion. The adsorption isotherm data agreed well with the Langmuir isotherm model, and the values of free energy E indicated that the adsorption nature of MNZ on the CMPs was physisorption. Increasing dispersion degree of the CMPs in MNZ solution resulted in greater adsorption. This work may provide fundamental guidance for the removal of antibiotics by CMPs.     

Effective diffusivities of BSA in cellulosic fiber beds measured with magnetic resonance imaging

The temporal and spatial evolution of concentration profiles of bovine serum albumin (BSA) in various cellulosic fiber beds is measured using magnetic resonance imaging. Effective diffusivities are calculated using a numerical one dimensional Fickian model to match experimental concentration profiles. Experimental values of the diffusivities are compared with predictions from a simple diffusion-adsorption model which accounts for porosity, tortuosity, and surface adsorption. BSA was found to have negligible adsorption in the concentration range studied, resulting in a simplified diffusion model based on fiber characteristics and geometry. Effective diffusivities agreed well with the predicted values and were within an order of magnitude of the estimated bulk diffusivity of BSA.     

3-D transient electrophoretic motion of a spherical particle in a T-shaped rectangular microchannel

This paper considers the electrophoretic motion of a spherical particle in an aqueous electrolyte solution in a T-shaped rectangular microchannel, where the size of the channel is close to that of the particle. This is a complicated transient process where the electric field, the flow field, and the particle motion are coupled together. A theoretical model was developed to investigate the influences of the applied electric potentials, the zeta potentials of the channel and the particle, and the size of the particle on the particle motion. A direct numerical simulation method using the finite element method is employed. This method employs a generalized Galerkin finite element formulation that incorporates both equations of the fluid flow and equations of the particle motion into a single variational equation where the hydrodynamic interactions are eliminated. The ALE method is used to track the surface of the particle at each time step. The numerical results show that the electric field in the T-shaped microchannel is influenced by the presence of the particle, and that the particle motion is influenced by the applied electric potentials and the zeta potentials of the channel and the particle. The path of the particle motion is dominated by the local electric field and the ratio of the zeta potential of the channel to that of the particle. The particle's velocity is also dependent on its size in a small channel.     

Mathematical modelling and simulation of adsorption processes at spherical microparticles.

A model for the adsorption process at spherical microparticles under transient diffusion conditions has been developed and solved using numerical simulation. This model allowed us to demonstrate that the system is controlled by two main dimensionless parameters: the adsorption rate constant ka' and the saturation parameter beta. Analytical models for the adsorption process at spherical microparticles under steady-state mass transport conditions have been derived. These models use previously developed empirical relationships for the calculation of the mass transfer coefficient (kc). The properties of the system were studied for both the case where mass transport is described by diffusion only and the case where it is the result of a coupled diffusion/convection process. These mathematical tools were then used to analyse the results obtained for the uptake of CuII by glassy carbon powder modified with the monomer L-cysteine methyl ester and to extract a minimum value for the adsorption rate constant which was found to be of the order of 10(-4) cm s(-1).     

A modified box model including charge regulation for protein adsorption in a spherical polyelectrolyte brush

Recent experiments showed significant adsorption of bovine serum albumin (BSA) in spherical polyelectrolyte brushes (SPB) consisting of polyacrylic acid, even for pH values above the isoelectric point of the protein, when both protein and polyion are negatively charged. To describe these experimental findings theoretically, we have constructed a spherical box model for an annealed brush consisting of a weak polyelectrolyte that includes the adsorption of BSA. At equilibrium the chemical potential of BSA in solution equals that at each location in the brush, while the net force on the polyions (including osmotic, stretching, and excluded volume terms) is zero at each location. Protein adsorption is predicted above the isoelectric point and--in agreement with experimental data--is a strong function of ionic strength and pH. Adsorption of protein in the brush is possible because the pH in the brush is below the isoelectric point and protein reverses its charge from negative to positive when it adsorbs.     

Approximate analytic expression for the dynamic electrophoretic mobility of a spherical colloidal particle in an oscillating electric field

An approximate analytic expression is derived for the dynamic electrophoretic mobility of a spherical charged colloidal particle in an electrolyte solution in an applied oscillating electric field. This expression, which takes into account the relaxation effects, is applicable for all values of zeta potential at large kappa a (kappa a > or = ca. 30) and omega/2pi < or = ca. 10 MHz, where kappa is the Debye-Hückel parameter, a is the particle radius, and omega is the frequency of the electric field. It is shown that the obtained mobility expression is in excellent agreement with the exact numerical results of Mangelsdorf and White (J. Chem. Soc., Faraday Trans. 1992, 88, 3567).     

Phenol adsorption from water solutions over microporous and mesoporous carbon surfaces: a real time kinetic study

This study illustrates the effect of the adsorbent porosity (activated carbon and high surface area graphite) on the phenol adsorption kinetics. We have developed an experimental system where on line analysis of the solution is carried out by an optic fiber probe introduced in the water solution and directly connected with the UV spectrometer. This experimental setup permits to be more precise in determining kinetic parameters, considering that measurements are taken each 20 seconds. Our results show that the choice of the particle diameter of the adsorbent is critical in the control of the adsorption process kinetic, while the porosity of the carbon materials appears to be less relevant.     

Short-time behavior of mixed diffusion-barrier controlled adsorption

This paper focuses on the short-time adsorption kinetics of nonionic surfactants onto water/air surfaces, analyzed in the context of the mixed diffusion-barrier controlled adsorption modeling framework. Specifically, we reconcile the apparent contradiction between theoretical prediction and experimental observations on the adsorption kinetics mechanism at short times: while the mixed diffusion-barrier controlled model predicts a barrier-controlled adsorption, as well as the impossibility of a diffusion-controlled adsorption at asymptotic short times, the short-time experimental dynamic surface tension (DST) behavior of many nonionic surfactants has been interpreted to result from diffusion-controlled adsorption at asymptotic short times. This is because the short-time experimental DST of these surfactants displays a t variation, which is considered as a fingerprint for the existence of diffusion-controlled adsorption, based on the short-time asymptotic behavior of the diffusion-controlled adsorption model. As a result of this interpretation, the fundamental physical nature of the energy barrier has been proposed to be associated with high surfactant surface concentrations. In this paper, we derive a new nonasymptotic short-time formalism of the mixed diffusion-barrier controlled model to describe surfactant adsorption onto a spherical pendant-bubble surface, including determining the ranges of time and surfactant surface concentration values where the short-time formalism is applicable. Based on this formalism, we find that one can expect to observe an apparent t variation of the DST at short times even for the mixed diffusion-barrier controlled adsorption model. We analyze the consequence of this finding by re-evaluating the existing notions of the energy barrier. We conclude that the energy barrier is associated with the adsorption of a single surfactant molecule onto a clean surface.     

Electrohydrodynamics of a drop under nonaxisymmetric electric fields

We consider the electrohydrodynamics of a spherical drop in a nonaxisymmetric electric field, which can be approximated by the sum of a uniform field and a linear straining field. We obtain the analytic solution of the three-dimensional flow fields inside and outside a drop for the Stokes flow regime by using Lamb's general solution and the leaky dielectric model. With the analytic solution, the dielectrophoretic migration velocity of a drop is obtained as a function of the type and the frequency of the imposed electric field. The direction of drop motion is found to be parallel to the dielectrophoretic force. The analytic solution is also used to investigate the characteristics of the interfacial flow under various nonaxisymmetric electric fields. While investigating the interfacial flow, we find a surface vortex structure under certain nonaxisymmetric electric fields, which is found to be related to the chaotic mixing inside the drop. Finally, we consider the chaotic features of three-dimensional flows inside the drop under static nonaxisymmetric electric fields.     

Impact of an error in the column hold-up time for correct adsorption isotherm determination in chromatography II. Can a wrong column porosity lead to a correct prediction of overloaded elution profiles?

The adsorption isotherm was determined for phenol in methanol/water on a C-8 stationary phase using frontal analysis in staircase mode, assuming different total column porosities, from 1 to 87%. Each set of adsorption isotherm data, with a certain column porosity, was fitted to various adsorption models and the generated parameters were used to calculate overloaded elution band profiles that were compared with experiments. It was found that the bi-Langmuir model had an optimum fit for a porosity that corresponds well with the value found experimentally. The adsorption energy distribution (AED) calculations and error analysis confirmed a bimodal energy distribution. It was also found that band profiles can be accurately predicted with a quite arbitrary chosen porosity, under prerequisite that a wrong but flexible adsorption model is chosen instead of the correct one. The latter result is very useful for quick optimizations of preparative separations where the exact value of the column porosity is not available.     

The simple procedure of the calculation of diffusion coefficient for adsorption on spherical and cylindrical adsorbent particles--experimental verification

A recently proposed simplified procedure for calculating the effective diffusion coefficient (D(e)) for adsorption on spherical and cylindrical adsorbent particles is now experimentally verified for adsorption systems: paracetamol-activated carbon. Adsorption kinetics was measured on nine carbons; for seven of them, measurements were taken at three temperatures. Since for adsorption on spherical adsorbent particles the approximate methods of D(e) calculation are already available in literature, only two systems have been studied, and the results of the new procedure are compared with those calculated from previously published methods. However, for cylinders the proposed method is the first simplification of this kind available in literature, thus, we focus our attention on the comparison of the results of the analytical approach with the simplified approaches for the systems where an adsorbent possesses cylindrically shaped granules. It is shown that for adsorption on spherical as well as on cylindrical adsorbent granules the proposed simplification leads to satisfactory results that, taking into account an experimental error, are practically the same as those obtained from exact time-consuming and mathematically advanced numerical fitting procedure. It is also shown that, for the studied carbons, the surface diffusion process dominates, and this explains the recently obtained correlation between the effective diffusion coefficient and the enthalpy of carbon immersion in water.     

Electroosmotic flow in a water column surrounded by an immiscible liquid

In this paper, we conducted numerical simulation of the electroosmotic flow in a column of an aqueous solution surrounded by an immiscible liquid. While governing equations in this case are the same as that in the electroosmotic flow through a microchannel with solid walls, the main difference is the types of interfacial boundary conditions. The effects of electric double layer (EDL) and surface charge (SC) are considered to apply the most realistic model for the velocity boundary condition at the interface of the two fluids. Effects on the flow field of ?-potential and viscosity ratio of the two fluids were investigated. Similar to the electroosmotic flow in microchannels, an approximately flat velocity profile exists in the aqueous solution. In the immiscible fluid phase, the velocity decreases to zero from the interface toward the immiscible fluid phase. The velocity in both phases increases with ?-potential at the interface of the two fluids. The higher values of ?-potential also increase the slip velocity at the interface of the two fluids. For the same applied electric field and the same ?-potential at the interface of the two fluids, the more viscous immiscible fluid, the slower the system moves. The viscosity of the immiscible fluid phase also affects the flatness of the velocity profile in the aqueous solution.     

Flow of solutions in thin capillaries coated with an adsorbed polyelectrolyte lyer

The flow of KCl solutions through thin quartz capillaries coated with an adsorbed layer of a cationic polyelectrolyte (CPE), poly(dimethyldiallylammonium chloride) (molecular mass M = 500000), is studied. It is found that the adsorption layer is soft and its thickness depends on shear stress generated by the liquid flow through the capillary. The hydrodynamic thickness of the CPE adsorption layer is 80–90 nm at low flow rates of a solution, and it decreases to values comparable with the experimental error at high flow rates. The dried adsorption layer appears to be hydrophobic (the advancing contact angle is about 80°); in these capillaries, the flow rate of a KCl solution is increased that can be interpreted as a solution slip on the surface of CPE adsorption layer. The long-term contact of the dried CPE adsorption layer with KCl solution, probably, results in the swelling of the adsorption layer, which is accompanied by a decrease in the contact angle and ζ potential of the adsorption layer surface as calculated from the streaming potential of the same solution.     

Electrokinetic motion of a charged colloidal sphere in a spherical cavity with magnetic fields

The magnetohydrodynamic (MHD) effects on the translation and rotation of a charged colloidal sphere situated at the center of a spherical cavity filled with an arbitrary electrolyte solution when a constant magnetic field is imposed are analyzed at the quasisteady state. The electric double layers adjacent to the solid surfaces may have an arbitrary thickness relative to the particle and cavity radii. Through the use of a perturbation method to the leading order, the Stokes equations modified with the electric∕Lorentz force term are dealt by using a generalized reciprocal theorem. Using the equilibrium double-layer potential distribution in the fluid phase from solving the linearized Poisson-Boltzmann equation, we obtain explicit formulas for the translational and angular velocities of the colloidal sphere produced by the MHD effects valid for all values of the particle-to-cavity size ratio. For the limiting case of an infinitely large cavity with an uncharged wall, our result reduces to the relevant solution for an unbounded spherical particle available in the literature. The boundary effect on the MHD motion of the spherical particle is a qualitatively and quantitatively sensible function of the parameters a∕b and κa, where a and b are the radii of the particle and cavity, respectively, and κ is the reciprocal of the Debye screening length. In general, the proximity of the cavity wall reduces the MHD migration but intensifies the MHD rotation of the particle.     

Adsorption of random copolymers by a selective layer: Monte Carlo studies

We use scaling arguments and computer simulations to investigate the adsorption of symmetric AB-random copolymers (RC) from a diluted solution onto a selective ABA layer. Depending on the ratio between the layer thickness and the size of excess blobs, d/xi, three regimes of RC adsorption are predicted. For large values of the layer thickness RC adsorption can be understood as adsorption on two selective interfaces where sequences of RC chains form bridges. When the layer thickness is of the order of xi, excess blobs are trapped in the layer and localize the copolymer chain strongly. If the layer thickness is very small a weak adsorption scenario is predicted where large loops are formed outside the layer. Our simulations using the bond fluctuation model are in good agreement with the scaling predictions. We show that chain properties display non-monotonous behavior with respect to the layer thickness with optimal values for d approximately xi. In particular, we discuss simulation results for density profiles, statistics of bridges, loops and tails formed by the adsorbed chains, as well as for the adsorption order parameter and free energy.     

Drug–Polymer Interactions in Hydrogel‐based Drug‐Delivery Systems: An Experimental and Theoretical Study

In drug‐delivery systems, drug transport is a key step, but the interpretation of the transport mechanism is still controversial. Here, we investigated a promising hydrogel library loaded with the anticonvulsant drug ethosuximide (ESM). The self‐diffusion coefficient of ESM was measured using two methods: a direct and advanced measurement with a pulsed field gradient spin‐echo (PFGSE) method, using an NMR spectrometer equipped with high‐resolution magic angle spinning (HR‐MAS) probe, and an indirect one based on fitting in vitro drug‐delivery data. Starting from the experimental data a mathematical model without fitted parameters was developed and all the phenomena involved, that is, adsorption and diffusion, were considered. At low drug concentrations, adsorption prevails and consequently the diffusivity in the gels is lower than that in water. At high drug concentrations, where all adsorption sites are saturated, the diffusion in the gels is similar to that in a water solution. This study may pave the way for better device design.     

Calculation of effective diffusion coefficient in a colloidal crystal by the finite-element method

The work is devoted to the calculation of effective diffusion coefficient of ions from the bulk solution to the electrode through a mask and the calculation of the distribution of the limiting current density over the electrode surface. A colloidal crystal, which is formed by orderly arranged monodispersed spherical particles, serves as a mask. It is shown that the diffusion of electroactive ions in the pores between spherical particles can be simulated by unit cells with rhombic, rectangular, or triangular cross-section. In the latter case, the cell side surface has no periodical boundaries. This simplifies significantly the numerical solution of the Laplace??s equation by the finite-element method. The effective diffusion coefficient in the bulk colloidal crystal is calculated at various values of its porosity. The calculated results agree well with the literature data. It is found that, for close-packed spherical particles, the relative effective diffusion coefficient in the bulk colloidal crystal is 0.16. The thicknesses of transient zones adjacent to the electrode surface and outer boundary of colloidal crystal and the effective diffusion coefficients for these zones are determined. The dependence of effective diffusion coefficient on the number of spherical particle layers in the colloidal crystal is obtained. The distribution of the limiting current density over the electrode surface is analyzed at various numbers of particle layers.     

Colloid filtration theory and the Happel sphere-in-cell model revisited with direct numerical simulation of colloids

The transport of colloids and bacterial cells through saturated porous media is a complex phenomenon involving many interrelated processes that are often treated via application of classical colloid filtration theory (CFT). This paper presents a numerical investigation of CFT from the Lagrangian perspective, to evaluate the role of some of the classical assumptions underlying the theory and to demonstrate a means to include processes relevant to bacterial transport that were inadequately characterized or neglected in the original formulation, including Brownian diffusion and potentially hysteretic potential functions. The methodology is based on conducting a Lagrangian trajectory analysis within Happel's sphere-in-cell porous media model to obtain the collection efficiency (eta), the frequency at which colloids or bacteria make contact with the solid phase of the porous medium. The Lagrangian framework of our model lends itself to mechanistic modeling of the biological processes that may be important in subsurface bacterial transport. The numerical study presented here focuses on the size range of bacterial colloids and smaller (down to 10 nm). Results of our model runs are in good agreement with the deterministic trajectory analysis of Rajagopalan and Tien (when diffusion is neglected) and in excellent agreement with the analytical solution to the Smoluchowski-Levich approximation of the convective-diffusion equation (when external forces and interception are neglected). Simple addition of our result for the deterministic eta to our result for the Smoluchowski-Levich eta matches the overall Rajagopalan and Tien eta to within 5% error or less for all cases studied. When we simulate diffusion and the deterministic forces together, our results diverge from the Rajagopalan and Tien eta as the particle size decreases, with discrepancies as large as 73%. These results suggest that accurate prediction of eta values for bacteria-sized (and all submicrometer) colloids requires simultaneous consideration of the primary transport mechanisms.     

Modeling nanoscopic formations of C60 on supporting substrates

Research into the controlled formation of nano-structured cluster-based layers on various types of supporting substrates occupies a very prominent place in both the experimental surface physics and in the newly emerging field of computational condensed matter physics, where such processes are modeled via computer-based numerical simulations at the atomic and molecular levels. One area of deep interest is the growth of nano-scale formations of C₆₀ fullerene on metallic and semi-conducting surfaces, which have potential applications in quantum-scale device fabrication. We review the field of C₆₀ adsorption on a variety of substrates, and then report on the highly accurate numerical simulations that we have performed to model the adsorption of this molecule on the Si and graphite substrates. We also report on the results of our computations of the scanning tunneling microscopy (STM)-like images of a C₆₀ molecule adsorbed on a graphite surface to show that no tip-induced states were responsible for the presence of extra features purported to have been observed in an experiment on this system.     

Numerical modeling of the elution peak profiles of retained solutes in supercritical fluid chromatography

In supercritical fluid chromatography (SFC), the significant expansion of the mobile phase along the column causes the formation of axial and radial gradients of temperature. Due to these gradients, the mobile phase density, its viscosity, its velocity, its diffusion coefficients, etc. are not constant throughout the column. This results in a nonuniform flow velocity distribution, itself causing a loss of column efficiency in certain cases, even at low flow rates, as they do in HPLC. At high flow rates, an important deformation of the elution profiles of the sample components may occur. The model previously used to account satisfactorily for the retention of an unsorbed solute in SFC is applied to the modeling of the elution peak profiles of retained compounds. The numerical solution of the combined heat and mass balance equations provides the temperature and the pressure profiles inside the column and values of the retention time and the band profiles of retained compounds that are in excellent agreement with independent experimental data for large value of mobile phase reduced density. At low reduced densities, the band profiles can strongly depend on the column axial distribution of porosity.