Transport of Carbamazepine,Ciprofloxacin and Sulfamethoxazole in Activated Carbon: Solubility and Relationships between Structure and Diffusional Parameters

The transport of carbamazepine, ciprofloxacin and sulfamethoxazole in the different pores of activated carbon in an aqueous solution is a dynamic process that is entirely dependent on the intrinsic parameters of these molecules and of the adsorbent. The macroscopic processes that take place are analyzed by interfacial diffusion and reaction models. Modeling of the experimental kinetic curves obtained following batch treatment of each solute at 2 µg/L in tap water showed (i) that the transport and sorption rates were controlled by external diffusion and intraparticle diffusion and (ii) that the effective diffusion coefficient for each solute, with the surface and pore diffusion coefficients, were linked by a linear relationship. A statistical analysis of the experimental data established correlations between the diffusional parameters and some geometrical parameters of these three molecules. Given the major discontinuities observed in the adsorption kinetics, the modeling of the experimental data required the use of traditional kinetic models, as well as a new kinetic model composed of the pseudo first or second order model and a sigmoidal expression. The predictions of this model were excellent. The solubility of each molecule below 60 °C was formulated by an empirical expression.     

Water evaporation from gel beads

Hydrogels are characterized by properties which make them ideal candidates for applications in several fields, such as drug delivery, biomedicine, and functional foods. Molecular diffusion out of a hydrogel matrix depends on their hydrodynamic radii and the mesh sizes within the matrix of the gel. A quantitative experimental and mathematical understanding of interactions, kinetics, and transport phenomena within complex hydrogel systems assists network design by identifying the key parameters and mechanisms that govern the rate and extent of solute release. In this article a calorimetric differential scanning calorimetry (DSC) study reports on the approach to parallel water effusion from a hydrogel matrix to the release of a model protein. The measurement of the water evaporation is taken as the simplest routine determination of a phenomenon that is basically due to a diffusive process through the porous structure of the gel and thermodynamically governed by the difference in the water chemical potential inside and outside of the bead. The analysis of the experimental calorimetric curves is made with the purpose of extracting several numerical parameters characteristic of each curve. The rationale is to develop a simple methodology to understand the release properties of the porous structure of the complex gel matrix by means of DSC.     

Diffusion and transfer of antibody proteins from a sugar-based hydrogel

Diffusion of antibody protein from hydrogel films and hydrogel encapsulated in a microcapillary was studied. Thin hydrogel films were formed by crosslinking 6-acryloyl-B-O-methylgalactoside withN,N’-methylene-bis-acrylamide and the diffusive transport of monoclonal antimouse IgG-FITC into and out of the hydrated films was measured. Diffusion coefficients in 2 and 4% crosslinked hydrogel films were measured. The measured diffusion constants determined for IgG in both the 2 and 4% hydrogel films were comparable to the free diffusion of IgG in bulk water (D _mean ∼ 10^-7cm²/s). In addition, 2% crosslinked hydrogels were prepared in a capillary tube and the transport of antimouse IgG-FITC into and out of the hydrated hydrogel was measured. Kinetic analysis indicated that the protein transport through the capillary hydrogel was faster than would be expected for a simple diffusion process. Finally, by utilizing the diffusion of antibody from the capillary hydrogel, transfer of antibody to a silica surface was demonstrated. A capillary hydrogel loaded with antimouse IgG-FITC was used to transfer the protein to a silica surface forming a 30-μm spot of antibody, which was imaged using fluorescence microscopy. These results may lead to the development of a nonlithographic method of patterning antibodies on surfaces for use in integrated microimmunosensors.     

The effect of obstacle conductivity and electric field on effective mobility and dispersion in electrophoretic transport: a volume averaging approach

The method of volume averaging has been used to determine the effective electrophoretic mobility and dispersion coefficients for molecular transport of point-like solutes in a two-phase porous medium where the electrical conductivity and the diffusion and mobility coefficients may vary in both phases. The formal theory, derived in previous work, is numerically evaluated for cases where the obstacle phase has a large or small conductivity relative to the fluid phase and where the diffusion coefficient of the solute in the obstacle phase can be large or small relative to that in the fluid phase. In agreement with previous Monte Carlo methods, the effective electrophoretic mobility is not a function of media conductivity or electric field when the obstacles are impermeable to solute transport or have small diffusion solute diffusion coefficients. However, the dispersion coefficient is a strong function of electric field and varies with obstacle conductivity when diffusive transport is small in the obstacles relative to the fluid. In contrast, the effective electrophoretic mobility is a function of electric field when conductivity of the obstacles is much larger than the fluid and when the obstacles are very permeable to solute but have low electrical conductivity.     

Dual-mode free volume model for diffusion of gas molecules in glassy polymers

The development of a new model for the diffusion of gas molecules in glassy polymers is presented which utilizes concepts from free volume theory and relies on a dual-mode interpretation of sorptive dilation in glassy polymers. Three assumptions are made in the development of the model. First, the free volume available for molecular transport processes is taken as constant below the glass transition temperature. Second, two populations of gas molecules are assumed to exist—one which contributes to the maintenance of an iso-free volume state upon sorptive dilation and one which does not contribute owing to sorption into regions of unrelaxed volume. Third, the former population is assumed to be mobile while the latter is not. The resulting model predicts, at constant temperature, a diffusion coefficient that is independent of solute volume fraction. This is in contrast to the widely used dual-mode sorption model with partial immobilization for gas transport in glassy polymers which leads to a diffusion coefficient that is dependent on solute mole fraction through the molar gas concentration. The new model is used to interpret gas transport data from permeation experiments for carbon dioxide, methane, and ethylene in three polycarbonates. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 1737–1746, 1997     

Comparison of three models for permeation of CO2/CH4 mixtures in poly(phenylene oxide)

Two models for the permeability of pure gases have been extended to include binary gas mixtures. The first is an extension of a pure gas permeability model, proposed by Petropoulos, which is based on gradients of chemical potential. This model predicts the permeability of components in a gas mixture solely on the basis of competition for sorption sites within the polymer matrix. The second mixed gas model follows an earlier analysis by Barrer for pure gases which includes the effects of saturation of Langmuir sites on the diffusion as well as the sorption processes responsible for permeation. This generalized “competitive sorption/diffusion” model includes the effect of each gas component on the sorption and diffusion of the other component in the mixture. The flux equations from these two models have been solved numerically to predict the permeability of gas mixtures on the basis of pure gas sorption and transport parameters. Both the mixed gas Petropoulos and competitive sorption/diffusion model predictions are compared with predictions from the earlier simple competitive sorption model based on gradients of concentration. An analysis of all three models is presented for the case of CO₂/CH₄ permeability in poly(phenylene oxide) (PPO). As expected, the competitive sorption/diffusion model predicts lower permeability than either of the models which consider only competitive sorption effects. The permeability depression of both CO₂ and CH₄ predicted by the competitive sorption/diffusion model is roughly twice that predicted by the competitive sorption model, whereas the mixed gas Petropoulos model predictions for both gases lie between the other two model predictions. For the PPO/CO₂/CH₄ system, the methane permeability data lie above the predictions of all three models, whereas CO₂ data lie below the predictions of all models. Consequently, the competitive sorption/diffusion model gives the most accurate prediction for CO₂, while the simple competitive sorption model is best for methane. The effects of mixed gas sorption, fugacity, and CO₂-induced dilation were considered and do not explain the inaccuracies of any of the models. The relatively small errors in mixed gas permeability predictions using either of the three models are likely to be related to “transport plasticization” of PPO owing to high levels of CO₂ sorption and its effect on polymer segmental motions and gas diffusivity.     

Sorbent material characterization using in‐tube extraction needles as inverse gas chromatography column

In‐tube extraction is a full automated enrichment technique that consists of a stainless‐steel needle, packed with sorbent material for the extraction of volatile and semivolatile compounds. In principle, all particulate sorbents used for enrichment in air or headspace analysis can be used. However, the selection of the sorbents is merely based on empirical considerations rather than on experimental data, which is caused by a lack of knowledge about the relevant physicochemical properties of the sorbent. Especially, the knowledge of hydrostatic, advective, diffusive, and dispersion mechanisms in addition to sorption enthalpies are important for combined transport and sorption models. To provide these missing parameters, we developed and evaluated a method in which an ordinary in‐tube extraction needle was employed directly as column for sorbent characterization by inverse gas chromatography. As probe compounds, benzene, ethyl acetate, and 3‐methyl‐1‐butanol were used to determine thermodynamic parameters such as sorption enthalpy, partitioning constant between the solid and gas phase, and kinetic parameters such as the diffusion coefficient, dispersion coefficient, and apparent permeability, exemplarily. As sorbent, three commercially available phases were characterized to demonstrate the applicability of the method.     

Thermoactuated diffusion control in soft matter nanofluidic devices

The diffusive transport rate in a soft matter nanofluidic device is controlled with a thermoactuated hydrogel valve. The device consists of three giant unilamellar vesicles linearly conjugated by lipid nanotubes, with a solution of the stimuli-responsive polymer poly(N-isopropyl acrylamide) (PNIPAAm) in the central vesicle. The valve states "high (transport) rate" and "low (transport) rate" are obtained by heat-activated switching between PNIPAAm's dissolved and compact aggregated states. We show that three parameters influence the diffusion rate within the device: the increase of the transport rate caused by a decrease in PNIPAAm concentration upon compaction, the temperature dependence of the buffer viscosity, and the volume excluded by the PNIPAAm hydrogel compartment.     

Analysis of transient permeation as a technique for determination of sorption and diffusion in supported membranes

Systematic membrane selection, process design as well as elucidation of structure–property relationships for pervaporation and vapor permeation require knowledge of sorption and diffusion properties. Direct measurement of sorption is not possible in the case of commercial membranes due to the presence of a support layer. Sorption measurements may also be difficult if the polymer is synthesized or crosslinked directly on the support and its properties are different from the bulk polymer. This work describes a technique to obtain sorption as well as diffusion parameters for supported membranes using transient permeation data. Computer simulations for transient permeation were carried out using sorption and diffusion data from the literature. It was demonstrated that the desired parameters could be estimated using data having a reasonable degree of error (±2%) by the least squares method. Alternatively, a time-lag analysis may be used instead of direct regression of the parameters by the least squares method. A general method for estimating the sorption as well as diffusion parameters using the time-lag and steady-state flux is described. Analytical solutions are derived for the various transport models, wherever possible.     

The use of moment theory to interpret diffusion and sieving measurements in terms of the pore size distribution in heteroporous membranes

Moment theory has been applied to model porous membranes to show that one can place reasonable bounds on the cumulative pore size distribution, the hindered diffusivity or the reflection coefficient of large solutes in a heteroporous membrane by measuring the diffusive permeability to a small solute, the hydraulic permeability and one or two additional transport characteristics. These additional measurements involve either the flux of a small solute at Pe1, the hindered diffusivity of a large solute or the reflection coefficient of a large solute at Peå1. Membrane heteroporosity is incroporated in the predicted bounds without requiring one to make any a priori assumptions about the nature of the pore size distribution. In this paper, the results from calculations performed with different model membranes containing log-normal pore size distributions are reported. A comparison of the results obtained with three different membranes shows that one can distinguish between membranes with the same average pore size but different pore size distributions by measuring either the hindered diffusion coefficient or the reflection coefficient of two different sized solutes. A comparison of the bounds on D and the bounds on σ predicted from different types of transport measurements shows that, under certain conditions, one can place tighter bounds on one transport characteristic by measuring a different one.     

Single-Microparticle Injection and Microabsorptiometry: Direct Analysis of Sorption Processes

Sorption processes of methylene blue in a single silica gel microparticle in an aqueous solution was kinetically analyzed by a new technique combined with the microcapillary injection/manipulation and microabsorptiometry of the single particle. The observed sorption rates were analyzed in terms of the solute concentration in water and the particle size. The sorption processes were governed by diffusion of the solute in the particle. Copyright 2000 Academic Press.     

A model incorporating reversible immobilization for sorption and diffusion in glassy polymers

A model incorporating reversible, bimolecular immobilization for diffusion and sorption in glassy polymers is developed. Sorption is considered to occur by two distinct mechanisms: ordinary diffusion-controlled sorption and sorption resulting from the immobilization of diffusing gas molecules by prexisting sites in the polymer. Expressions are obtained for equilibrium sorption, transient sorption, and time lag. The effects of kinetic parameters of the model are illustrated and discussed.     

Segmental mobility model for diffusion of gases in polymers

Diffusion of small molecules in polymers is described quantitatively in terms of segmental mobility processes. The diffusion coefficient depends on a diffusive jump length, which is characteristic of the polymer, and a jump frequency, which is equated to the segmental mobility rate. The presence of a particular solute increases mobility of the surrounding polymer segments by a predictable amount, which is related to the partial molar volume of the solute. The theory is fit to experimental diffusion data, and partial molar volumes are calculated from the fitting parameters. Good agreement with experimental partial molar volumes is obtained.     

Dynamics of the sorption of phosphatidylcholine by mesoporous composites based on MCM-41

The possibility of predicting the breakthrough curves of a phospholipid (PL) during its sorption by mesoporous composites based on MCM-41 using models of the dynamics of sorption that consider the kinetics of adsorption (the Thomas model) and mixed diffusion (the asymptotic model) is demonstrated using phosphatidylcholine (PC) as an example. The effect the kinetic parameters have on the tailing of the sorption front with respect to the mixed diffusion limitation of the sorption of nonpolar biologically active substances (BASes) is shown. It is found that the ordered structure of composite materials based on MCM-41 ensures a high rate of mass transfer and thus little tailing of the sorption front, when compared to sorbents with a lower degree of order (silica gel and polymer materials) during the sorption of a phospholipid under dynamic conditions. Based on calculations of the parameter of pattern Λ under the conditions of the dynamic mode of sorption in mixed diffusion kinetics, it is shown that the sorption of phosphatidylcholine from hexane solutions by mesoporous composites based on MCM-41 allows the sorption chromatographic process to proceed in the most advantageous (quasi-equilibrium) mode.     

The Role of Drug–Drug Interactions in Hydrogel Delivery Systems: Experimental and Model Study

To address the increasing need for improved tissue substitutes, tissue engineering seeks to create synthetic, three‐dimensional scaffolds made from polymeric materials able to incorporate cells and drugs. The interpretation of transport phenomena is a key step, but comprehensive theoretical data is still missing and many issues related to these systems are still unsolved. In particular, the contribution of solute–solute interactions is not yet completely understood. Here, we investigate a promising agar–carbomer (AC) hydrogel loaded with sodium fluorescein (SF), a commonly used drug mimetic. The self‐diffusion coefficient of SF in AC formulations was measured by using high resolution magic angle spinning NMR spectroscopy (HR‐MAS NMR). Starting from experimental data, a complete overview on SF transport properties is provided, in particular a mathematical model that describes and rationalizes the differences between gel and water environments is developed and presented. The hydrogel molecular environment is able to prevent SF aggregation, owing to the adsorption mechanism that reduces the number of monomers available for oligomer formation at low solute concentration. Then, when all adsorption sites are saturated free SF molecules are able to aggregate and form oligomers. The model predictions satisfactorily match with experimental data obtained in water and the gel environment, thus indicating that the model presented here, despite its simplicity, is able to describe the key phenomena governing device behavior and could be used to rationalize experimental activity.     

Modulation of drug transport properties by multicomponent diffusion in surfactant aqueous solutions

Diffusion coefficients of drug compounds are crucial parameters used for modeling transport processes. Interestingly, diffusion of a solute can be generated not only by its own concentration gradient but also by concentration gradients of other solutes. This phenomenon is known as multicomponent diffusion. A multicomponent diffusion study on drug-surfactant-water ternary mixtures is reported here. Specifically, high-precision Rayleigh interferometry was used to determine multicomponent diffusion coefficients for the hydrocortisone-tyloxapol-water system at 25 degrees C. For comparison, diffusion measurements by dynamic light scattering were also performed. In addition, drug solubility was measured as a function of tyloxapol concentration, and drug-surfactant thermodynamic interactions using the two-phase partitioning model were characterized. The diffusion results are in agreement with a proposed coupled multicomponent diffusion model for ternary mixtures relevant to nonionic drug and surfactant molecules. Theoretical examination of diffusion-based drug transport in the presence of concentration gradients of micelles shows that drug fluxes and drug concentration profiles are significantly affected by coupled multicomponent diffusion. This work provides guidance for the development of accurate models of diffusion-based controlled release in multicomponent systems and for the applications of micelle concentration gradients to the modulation of diffusion-based drug transport.     

Glucose diffusivity and porosity in silica hydrogel based on organofunctional silanes

The silica hydrogels prepared at physiological conditions were characterized with respect to the glucose diffusion properties and the porosity by employing various approaches. A diffusion coefficient of glucose in silica hydrogel in the range of 2 × 10⁻¹⁰ m² s⁻¹ was determined by two complementary techniques based on the glucose ingress and egress, respectively. The confocal laser scanning microscopy in a time-lapse imaging mode was employed to measure the ingress of fluorescently labeled glucose analogue inside the hydrogel. In addition, a method for direct glucose release from the hydrogel was established. The simple diffusion model based on the Fickian diffusion and Ritger–Peppas theory were employed for evaluation of diffusion coefficients, respectively. The BET analysis and permeation of fluorescently labeled dextrans of various molecular weights were used to characterize the porosity of silica hydrogel. The radius of pores accessible for diffusion of dextran molecules in prepared silica hydrogel ranges between 1 and 6 nm.     

Solute distribution coupled with laminar flow in wide-bore capillaries: what can be separated without chemical or physical fields?

Solute diffusion coupled with an orthogonal laminar flow has been systematically studied with wide-bore capillaries to establish its limitations and reveal its potentials as separation methodology requiring neither chemical nor physical interactions. Simulations based on the advection-diffusion equation in a cylindrical coordinate system indicate several important features of this potentially useful method: (1) if a solute diffuses over the entire cross-section of the capillary before it is eluted from the capillary, it behaves as a diffusive solute and gives a Gaussian-shaped peak (diffusion peak) having an apex at the traveling time of the average flow; (2) when a solute is poorly (or not) diffusive, a new peak appears with an apex at the elution time of the maximum flow (non-diffusion peak); (3) these two peaks are simultaneously detected for intermediately diffusive solutes; (4) the transformation from the diffusion to non-diffusion peak occurs when the solute diffuses over the distance 0.86 times as large as the capillary radius before it leaves the capillary. These results of simulations are consistent with experimental results for selected solutes having various diffusivities. This method has proved useful particularly for the evaluation of diffusion coefficients of poorly diffusive solutes. Separation of PS particles having different sizes is also attempted.