Diffusion measurement in gels

Non-Steady-State Fickian Diffusion Models Decrease the Estimated Gel Layer Diffusion Coefficient Uncertainty for Diffusive Gradients in Thin-Films Passive Samplers

Mass transport in diffusive gradients in thin-film passive samplers is restricted to diffusion through a gel layer of agarose or agarose cross-linked polyacrylamide (APA). The gel layer diffusion coefficient, DGel, is typically determined using a standard analysis (SA) based on Fick's first law from two-compartment diffusion cell (D-Cell) tests. The SA assumes pseudo-steady-state flux, characterized by linear sink mass accumulation-time profiles with a typical threshold R2 ≥ 0.97. In 72 D-Cell tests with nitrate, 63 met this threshold, but the SA-determined DGel ranged from 10.1 to 15.8 × 10-6 cm2·s-1 (agarose) and 9.5 to 14.7 × 10-6 cm2·s-1 (APA). A regression model developed with the SA to account for the diffusive boundary layer had 95% confidence intervals (CIs) on DGel of 13 to 18 × 10-6 cm2·s-1 (agarose) and 12 to 19 × 10-6 cm2·s-1 (APA) at 500 rpm. A finite difference model (FDM) developed based on Fick's second law with non-steady-state (N-SS) flux decreased uncertainty in DGel tenfold. The FDM-captured decreasing source compartment concentrations and N-SS flux in the D-Cell tests and, at 500 rpm, the FDM-determined DGel ± 95% CIs were 14.5 ± 0.2 × 10-6 cm2·s-1 (agarose) and 14.0 ± 0.3 × 10-6 cm2·s-1 (APA), respectively.

Desorption kinetics of antipsychotic drugs from sandy sediments by diffusive gradients in thin-films technique

Dynamic processes of organic contaminants in sediments can have important toxicological implications in aquatic systems. The current study used diffusive gradients in thin-films (DGT) devices in sandy sediments spiked with nine antipsychotics and in field sandy sediments. Samplers were deployed for 1 to 30 days to determine the flux of these compounds to DGT devices and the exchange rates between the porewater and sediment solid phase. The results showed a continuous removal of antipsychotics to a binding gel and induced a mobile flux from the DGT device to the adjacent sediment solution. A dynamic model, DGT-induced fluxes in soils and sediments, was used to derive rate constants of resupply of antipsychotics from solid phase to aqueous phase (response time, T_c) and distribution coefficients for labile antipsychotics. The largest labile pool was found for lamotrigine and carbamazepine in spiked sediments. Carbamazepine, clozapine, citalopram, and lamotrigine were resupplied rapidly by sediments with T_c (25-30 min). T_c values of bupropion and amitriptyline were the longest (≈5 h), which exhibited slow desorption rates in sediments. In field sediments, high resupply was found for carbamazepine and lamotrigine, which did not show higher labile pool. The T_c values were obviously higher in the filed sediments (52-171 h). Although the adsorption process is dominant for most studied antipsychotics in both spiked sediments and field sediments, the kinetic resupply of antipsychotic compounds may not be accurately estimated by laboratory-controlled incubation experiments. More studies are needed to explore the mechanisms of desorption kinetics by using in situ DGT technique in the field.

A novel passive sampling and sequential extraction approach to investigate desorption kinetics of emerging organic contaminants at the sediment-water interface

Forms of organic contaminants is an important driver of bioavailable fraction and desorption kinetics of pollutants binding to sediments. To determine fluxes and resupply of nine environmentally-relevant antipsychotic drugs, which are emerging pollutants that can have adverse effects on aquatic organisms, interface passive samplers of diffusive gradients in thin films (DGT) were deployed for 21 days, in situ at the sediment-water interface in submerged sandy riverbank sediments. At each deployment time, samples of sediment were collected and subjected to consecutive extraction of pore water, as well as rapidly-desorbing (labile), stable-desorbing, and bound residue fractions. Concentrations of antipsychotic drugs decreased with sediment depth with the greatest concentrations observed in the top 2 cm. Positive fluxes of antipsychotic drugs were observed from sediment to surface water. The dynamic fraction transfer model indicated that the labile fraction can be resupplied with a lag time (> 21 d). When results were further interpreted using the DGT-induced fluxes in soils and sediments (DIFS) model, partial resupply of antipsychotic drugs from sediment particles to porewater was demonstrated. Desorption occurred within the entirety of the observed 15 cm depth of sediment. Fastest rates of resupply were found for carbamazepine and lamotrigine. Size of the labile pool estimated by the DIFS model did not fully explain the observed resupply, while a first-order three-compartment kinetic model for the fast-desorbing fraction can be used to supplement DIFS predictions with estimations of labile pool size.

Solute Diffusion into Polymer Swollen by Supercritical CO2 by High-Pressure Electron Paramagnetic Resonance Spectroscopy and Chromatography

High-pressure electron paramagnetic resonance (EPR) was used to measure translational diffusion coefficients (D_tr) of a TEMPONE spin probe in poly(D,L-lactide) (PDLLA) and swollen in supercritical CO₂. D_tr was measured on two scales: macroscopic scale (>1 μm), by measuring spin probe uptake by the sample; and microscopic scale (<10 nm), by using concentration-dependent spectrum broadening. Both methods yield similar translational diffusion coefficients (in the range 5-10 × 10^-12 m²/s at 40-60 °C and 8-10 MPa). Swollen PDLLA was found to be homogeneous on the nanometer scale, although the TEMPONE spin probe in the polymer exhibited higher rotational mobility (τ_corr = 6 × 10^-11 s) than expected, based on its D_tr. To measure distribution coefficients of the solute between the swollen polymer and the supercritical medium, supercritical chromatography with sampling directly from the high-pressure vessel was used. A distinct difference between powder and bulk polymer samples was only observed at the start of the impregnation process.

How to measure diffusion coefficients in biofilms: A critical analysis

Biofilm and granular sludge processes depend on diffusion of substrates. Despite their importance for the kinetic description of biofilm reactors, biofilm diffusion coefficients reported in literature vary greatly. The aim of this simulation study was to determine to what extent the methods that are used to measure diffusion coefficients contribute to the reported variability. Granular sludge was used as a case study. Six common methods were selected, based on mass balances and microelectrodes. A Monte Carlo simulation was carried out to determine the theoretical precision of each method, considering the uncertainty of various experimental parameters. A model-based simulation of a diffusion experiment was used to determine the theoretical accuracy as a result of six sources of error: solute sorption, biomass deactivation, mass transfer boundary layer, granule roughness, granule shape, and granule size distribution. Based on the Monte Carlo analysis, the relative standard deviation of the different methods ranged from 5% to 61%. In a theoretical experiment, the six error sources led to an 37% underestimation of the diffusion coefficient. This highlights that diffusion coefficients cannot be determined accurately with existing experimental methods. At the same time, the need for measuring precise diffusion coefficients as input value for biofilm modeling can be questioned, since the output of biofilm models has a limited sensitivity toward the diffusion coefficient.

Calibration of organic-diffusive gradients in thin films (o-DGT) passive samplers for perfluorinated alkyl acids in water

The application of the organic-diffusive gradients in thin films (o-DGT) passive sampling technique for the monitoring of per- and polyfluoroalkyl substances (PFAS) in the environment is still limited. Six common PFAS with different chain lengths were evaluated in water by o-DGT. Measured diffusion coefficients (D) in agarose and polyacrylamide diffusive gels ranged from 4.55-8.63 × 10^-6 cm² s^-1 and 3.85-7.00 × 10^-6 cm² s^-1 at 23 °C, respectively. Experimental sampling rates (Rs) for both agarose- and polyacrylamide-WAX sampler configurations were within 22% relative error of D-based Rs for four of the PFAS. Larger differences for perfluorobutanesulfonic acid (PFBS) and perfluoroundecanoic acid (PFUnDA) ranged from 36% to 56%. In general, in-situ Rs can be predicted using measured D-values for perfluorinated alkyl acids. The mass accumulation of six PFAS in two o-DGT configurations was linear over 21 days (R² ≥ 0.97). Diffusion and uptake of o-DGT depended on the gel type and specific PFAS. Field demonstrations of o-DGT with WAX and HLB binding gels and polyacrylamide diffusive gels (not prone to biodegradation) found 0.3-19.5 ng L^-1 of PFAS in rivers near industrial areas around Guangzhou and Foshan, China, with no apparent differences between the two co-deployed samplers. This study demonstrates that the configurations of o-DGT tested provide a cost-effective monitoring tool for measuring perfluorinated alkyl acids in aquatic systems, in particular the four PFAS for which reasonable correlations were observed.

Diffusion coefficients of polar organic compounds in agarose hydrogel and water and their use for estimating uptake in passive samplers

Diffusion coefficient (D) is an important parameter for prediction of micropollutant uptake kinetics in passive samplers. Passive samplers are nowadays commonly used for monitoring trace organic pollutants in different environmental matrices. Samplers utilising a hydrogel layer to control compound diffusion are gaining popularity. In this work we investigated diffusion of several perfluoroalkyl substances, currently used pesticides, pharmaceuticals and personal care products in 1.5% agarose hydrogel by measuring diffusion coefficients using two methods: a diffusion cell and a sheet stacking technique. Further, diffusion coefficients in water were measured using Taylor dispersion method. The sheet stacking method was used to measure D at 5, 12, 24, and 33 °C in order to investigate temperature effect on diffusion. Median D values ranged from 2.0 to 8.6 × 10^-6 cm² s^-1 and from 2.1 to 8.5 × 10^-6 cm² s^-1 for the diffusion cell and sheet stack methods respectively. For most compounds, the variability between replicates was higher than the difference between values obtained by the two methods. Rising temperature from 10 to 20 °C increases the diffusion rate by the factor of 1.41 ± 0.10 in average. In water, average D values ranged from 3.03 to 10.0 × 10^-6 cm² s^-1 and were comparable to values in hydrogel, but some compounds including perfluoroalkyl substances with a long aliphatic chain could not be evaluated properly due to sorptive interactions with capillary walls in the Taylor dispersion method. Sampling rates estimated using the measured D values were systematically higher than values estimated from laboratory sampler calibration in our previously published study, by the factor of 2.2 ± 1.0 in average.

Protein diffusion from microwells with contrasting hydrogel domains

Understanding and controlling molecular transport in hydrogel materials is important for biomedical tools, including engineered tissues and drug delivery, as well as life sciences tools for single-cell analysis. Here, we scrutinize the ability of microwells-micromolded in hydrogel slabs-to compartmentalize lysate from single cells. We consider both (i) microwells that are "open" to a large fluid (i.e., liquid) reservoir and (ii) microwells that are "closed," having been capped with either a slab of high-density polyacrylamide gel or an impermeable glass slide. We use numerical modeling to gain insight into the sensitivity of time-dependent protein concentration distributions on hydrogel partition and protein diffusion coefficients and open and closed microwell configurations. We are primarily concerned with diffusion-driven protein loss from the microwell cavity. Even for closed microwells, confocal fluorescence microscopy reports that a fluid (i.e., liquid) film forms between the hydrogel slabs (median thickness of 1.7 μm). Proteins diffuse from the microwells and into the fluid (i.e., liquid) layer, yet concentration distributions are sensitive to the lid layer partition coefficients and the protein diffusion coefficient. The application of a glass lid or a dense hydrogel retains protein in the microwell, increasing the protein solute concentration in the microwell by ∼7-fold for the first 15 s. Using triggered release of Protein G from microparticles, we validate our simulations by characterizing protein diffusion in a microwell capped with a high-density polyacrylamide gel lid (p > 0.05, Kolmogorov-Smirnov test). Here, we establish and validate a numerical model useful for understanding protein transport in and losses from a hydrogel microwell across a range of boundary conditions.

Impermeable Robust Hydrogels via Hybrid Lamination

Hydrogels have been proposed for sensing, drug delivery, and soft robotics applications, yet most of these materials suffer from low mechanical robustness and high permeability to small molecules, limiting their widespread use. This study reports a general strategy and versatile method to fabricate robust, highly stretchable, and impermeable hydrogel laminates via hybrid lamination of an elastomer layer bonded between hydrogel layers. By controlling the layers' composition and thickness, it is possible to tune the stiffness of the impermeable hydrogels without sacrificing the stretchability. These hydrogel laminates exhibit ultralow surface coefficients of friction and, unlike common single-material hydrogels, do not allow diffusion of various molecules across the structure due to the presence of the elastomer layer. This feature is then used to release different model drugs and, in a subsequent experiment, to sense different pH conditions on the two sides of the hydrogel laminate. A potential healthcare application is shown using the presented method to coat medical devices (catheter, tubing, and condom) with hydrogel, to allow for drug release and sensing of environmental conditions for gastrointestinal or urinary tract.

Tuning mass transport in magnetic nanoparticle-filled viscoelastic hydrogels using low-frequency rotating magnetic fields

This study investigates the response of magnetic nanoparticles (MNPs), dispersed in a viscoelastic hydrogel, to an external rotating magnetic field (RMF) for the purpose of developing a new class of magneto-responsive materials with tunable mass transport properties. Ferrogels were prepared by chemical cross-linking and polymerization of acrylamide in colloidal dispersions of thermally blocked MNPs of cobalt ferrite. Magnetization measurements of ferrogels in a swollen state revealed a transitional state from ferromagnetism to superparamagnetism through the shrinkage of hysteresis loops and the reduction of remanent magnetization. A quantitative analysis of magnetization data indicated the existence of hydrodynamically free MNPs, susceptible to Brownian relaxation along with the blocked ones. It was found through rheological analysis that inclusion of MNPs within the polymer matrix significantly alters the ferrogel's elasticity. At low chemical crosslinking ratios, MNPs improve elasticity through the formation of physical crosslinks ensued by reduction in the fraction of the free MNPs. As the crosslinking ratio was increased, the polymer network showed a tendency toward blockage of more MNPs. Effective diffusion coefficients in both particle-free hydrogels and ferrogels were obtained by measuring the release kinetics of a model compound in the absence and presence of an external low-frequency RMF. Experimental results showed that conversion of magnetic energy to kinetic energy by rotational movement of the free MNPs in a RMF escalates mass transport provided that hydrodynamically free MNPs are available within the ferrogels. The effectiveness of excitation by a RMF showed correlation with the density of free MNPs. Release experiments at constant RMF intensity and various frequencies revealed augmentation of effective diffusivities as the frequency was increased from 10 to 75 Hz.

Diffusion of macromolecules in a polymer hydrogel: from microscopic to macroscopic scales

To gain insight into the fundamental processes determining the motion of macromolecules in polymeric matrices, the dynamical hindrance of polymeric dextran molecules diffusing as probe through a polyacrylamide hydrogel is systematically explored. Three complementary experimental methods combined with Brownian dynamics simulations are used to study a broad range of dextran molecular weights and salt concentrations. While multi-parameter fluorescence image spectroscopy (MFIS) is applied to investigate the local diffusion of single molecules on a microscopic length scale inside the hydrogel, a macroscopic transmission imaging (MTI) fluorescence technique and nuclear magnetic resonance (NMR) are used to study the collective motion of dextrans on the macroscopic scale. These fundamentally different experimental methods, probing different length scales of the system, yield long-time diffusion coefficients for the dextran molecules which agree quantitatively. The measured diffusion coefficients decay markedly with increasing molecular weight of the dextran and fall onto a master curve. The observed trends of the hindrance factors are consistent with Brownian dynamics simulations. The simulations also allow us to estimate the mean pore size for the herein investigated experimental conditions. In addition to the diffusing molecules, MFIS detects temporarily trapped molecules inside the matrix with diffusion times above 10 ms, which is also confirmed by anisotropy analysis. The fraction of bound molecules depends on the ionic strength of the solution and the charge of the dye. Using fluorescence intensity analysis, also MTI confirms the observation of the interaction of dextrans with the hydrogel. Moreover, pixelwise analysis permits to show significant heterogeneity of the gel on the microscopic scale.

Diffusion of Oligonucleotides from within Iron-Cross-Linked, Polyelectrolyte-Modified Alginate Beads: A Model System for Drug Release

An analytical model to describe diffusion of oligonucleotides from stable hydrogel beads is developed and experimentally verified. The synthesized alginate beads are Fe(3+) -cross-linked and polyelectrolyte-doped for uniformity and stability at physiological pH. Data on diffusion of oligonucleotides from inside the beads provide physical insights into the volume nature of the immobilization of a fraction of oligonucleotides due to polyelectrolyte cross-linking, that is, the absence of a surface-layer barrier in this case. Furthermore, the results suggest a new simple approach to measuring the diffusion coefficient of mobile oligonucleotide molecules inside hydrogels. The considered alginate beads provide a model for a well-defined component in drug-release systems and for the oligonucleotide-release transduction steps in drug-delivering and biocomputing applications. This is illustrated by destabilizing the beads with citrate, which induces full oligonucleotide release with nondiffusional kinetics.

Diffusion of macromolecules in self-assembled cellulose/hemicellulose hydrogels

Cellulose hydrogels are extensively applied in many biotechnological fields and are also used as models for plant cell walls. We synthesised model cellulosic hydrogels containing hemicelluloses, as a biomimetic of plant cell walls, in order to study the role of hemicelluloses on their mass transport properties. Microbial cellulose is able to self-assemble into composites when hemicelluloses, such as xyloglucan and arabinoxylan, are present in the incubation media, leading to hydrogels with different nano and microstructures. We investigated the diffusivities of a series of fluorescently labelled dextrans, of different molecular weight, and proteins, including a plant pectin methyl esterase (PME), using fluorescence recovery after photobleaching (FRAP). The presence of xyloglucan, known to be able to crosslink cellulose fibres, confirmed by scanning electron microscopy (SEM) and (13)C NMR, reduced mobility of macromolecules of molecular weight higher than 10 kDa, reflected in lower diffusion coefficients. Furthermore PME diffusion was reduced in composites containing xyloglucan, despite the lack of a particular binding motif in PME for this polysaccharide, suggesting possible non-specific interactions between PME and this hemicellulose. In contrast, hydrogels containing arabinoxylan coating cellulose fibres showed enhanced diffusivity of the molecules studied. The different diffusivities were related to the architectural features found in the composites as a function of polysaccharide composition. Our results show the effect of model hemicelluloses in the mass transport properties of cellulose networks in highly hydrated environments relevant to understanding the role of hemicelluloses in the permeability of plant cell walls and aiding design of plant based materials with tailored properties.

Comparative diffusivity measurements for alginate-based atomized and inkjet-bioprinted artificial cells using fluorescence microscopy

Radial diffusivity profiles of atomized (MC, d = 1800 ± 200 µm) and inkjet-printed (MI, d = 40 ± 5 µm) alginate-based artificial cells have been generated using 2D Fluorescence Microscopy. The passive outward diffusion of FITC-Dextrans from MIs (0.5% LV alginate/15% CaCl2 coated with 0.5% Chitosan) and MCs (1.5% MV alginate/1.5% CaCl2) was measured and quantified using a Fickian model. As an expected outcome of miniaturization, the ratios of the outer layer diffusivities defined as D(MIout)/D(MCout) were 4.25 and 5.07 respectively for the 4 and 70 kDa markers, indicative of the enhanced diffusive potential of the miniaturized capsules.

Determination of local diffusion properties in heterogeneous biomaterials

The coupling between structure and diffusion properties is essential for the functionality of heterogeneous biomaterials. Structural heterogeneity is defined and its implications for time-dependent diffusion are discussed in detail. The effect of structural heterogeneity in biomaterials on diffusion and the relevance of length scales are exemplified with regard to different biomaterials such as gels, emulsions, phase separated biopolymer mixtures and chocolate. Different diffusion measurement techniques for determination of diffusion properties at different length and time scales are presented. The interplay between local and global diffusion is discussed. New measurement techniques have emerged that enable simultaneous determination of both structure and local diffusion properties. Special emphasis is given to fluorescence recovery after photobleaching (FRAP). The possibilities of FRAP at a conceptual level is presented. The method of FRAP is briefly reviewed and its use in heterogeneous biomaterials, at barriers and during dynamic changes of the structure is discussed.

Mathematical modeling of molecular diffusion through mucus

The rate of molecular transport through the mucus gel can be an important determinant of efficacy for therapeutic agents delivered by oral, intranasal, intravaginal/rectal, and intraocular routes. Transport through mucus can be described by mathematical models based on principles of physical chemistry and known characteristics of the mucus gel, its constituents, and of the drug itself. In this paper, we review mathematical models of molecular diffusion in mucus, as well as the techniques commonly used to measure diffusion of solutes in the mucus gel, mucus gel mimics, and mucosal epithelia.

Measurement of Protein Diffusion Through Poly(d,l-Lactide-Co-Glycolide)

A novel method was developed for studying the diffusion of proteins through poly(D,L-lactide-co-glycolide) (PLG), using a diffusion cell. To develop improved formulations for the controlled release of encapsulated drugs it is important to understand the underlying release mechanisms. When using low-molecular-weight PLG as the release-controlling polymer, diffusion through the pores is often proposed as the main release mechanism. The experimental set-up and method of determining the diffusion coefficient were thoroughly evaluated with regard to the reliability and the influence of the stirring rate. A procedure for spraying thin films of PLG onto a filter, which could be placed in the diffusion cell, was optimized. The method was then applied to the determination of the diffusion coefficient of human growth hormone (hGH) through a PLG film. The results show that the method enables measurements of the diffusion coefficient through the polymer film. Neither the stirring rate nor the concentration of hGH influenced the diffusion coefficient. The diffusion coefficient of hGH through degraded PLG films was 5.0 x 10(-13) m2/s, which is in the range that could be expected, i.e., several orders of magnitude smaller than its the diffusivity in pure water. The reproducibility was good, considering the dynamic properties of PLG, i.e., the difference in diffusion coefficients, at, for example, different stages of degradation and for different compositions of PLG, is expected to be much higher. The variation is probably also present in PLG films used for controlled-release formulations. Although the PLG film contains a large amount of water, a considerable time elapsed before pores of sufficient size formed and diffusion through the film started. In two-component diffusion experiments, the difference in diffusion rate did not correspond to the difference in molecular weight of the solutes, indicating a size exclusion effect. This method can be used to study the effect of changes in the formulation specification. By studying the change in the diffusion coefficient through the degradation process of PLG, or similar polymers, a better understanding of diffusion and, thus, also release mechanisms can be obtained.

Influence of kappa-carrageenan gel structures on the diffusion of probe molecules determined by transmission electron microscopy and NMR diffusometry

The influence of the microstructures of different kappa-carrageenan gels on the self-diffusion behavior of poly(ethylene glycol) (PEG) has been determined by nuclear magnetic resonance (NMR) diffusometry and transmission electron microscopy (TEM). It was found that the diffusion behavior was determined mainly by the void size, which in turn was defined by the state of aggregation of the kappa-carrageenan. The kappa-carrageenan concentration was held constant at 1 w/w%, and the aggregation was controlled by the amount of potassium and/or sodium chloride and, for samples containing potassium, also by the cooling rate. Gels containing potassium formed microstructures where kappa-carrageenan strands are rather evenly distributed over the image size, while sodium gels formed dense biopolymer clusters interspersed with large openings. In a gel with small void sizes, relatively slow diffusion was found for all PEG sizes investigated. Extended studies of the self-diffusion behavior of the 634 g mol(-)(1) PEG showed that there is a strong time dependence in the measured PEG diffusion. An asymptotic lower time limit of the diffusion coefficient was found in all gels when the diffusion observation time was increased. According to the ratio, D/D(0), where D(0) is the diffusion coefficient in D(2)O and D is the diffusion coefficient in the gels, the gels could be divided into three classes: small, medium, and large voids. For quenched kappa-carrageenan solutions with salt concentrations of 20 mM K(+), 100 mM K(+), or 20 mM K(+)/200 mM Na(+) as well as slowly cooled solutions with only 20 mM K(+), D/D(0) ratios between 0.18 and 0.29 were obtained. By quenching a kappa-carrageenan solution with 100 mM K(+), the D/D(0) was 0.5, while D/D(0) ratios between 0.9 and 1 were obtained in a quenched solution with 250 mM Na(+) and slowly cooled samples with 20 mM K(+)/200 mM Na(+) or 250 mM Na(+).

Measurement of dye diffusion in scattering tissue phantoms using dual-wavelength low-coherence interferometry

We demonstrate low-coherence interferometry (LCI) for dye diffusion measurements in scattering tissue phantoms. The diffusion coefficient of a phthalocyanine dye in 1.5% agar gel containing scattering Intralipid was measured using a dual-wavelength interfero-meter. One wavelength was matched to the absorption peak of the dye at 675 nm. The other, 805 nm, was not affected by the dye, and was used to correct for varying sample scattering as a function of depth, assuming a constant ratio between scattering at the two wavelengths. The same wavelength dependence of scattering is assumed for the entire sample, but no a priori knowledge about the amount of scattering is needed. The dye diffusion coefficient was estimated by fitting a mathematical model of the interferometer signal to the measured LCI envelope. We compare results obtained using both a constant-scattering and a depth-resolved-scattering approach to determine the sample scattering. The presented method provides robust estimation of the diffusion coefficient when spatial resolution in determining the depth-resolved scattering is varied. Results indicate that the method is valid for samples having continuous spatial variations in the scattering coefficient over lengths as short as the coherence length of the probing light. The method allows in situ characterization of diffusion in scattering media.

A new scleroglucan/borax hydrogel: swelling and drug release studies

The aim of the work was the characterization of a new polysaccharidic physical hydrogel, obtained from Scleroglucan (Sclg) and borax, following water uptake and dimension variations during the swelling process. Furthermore, the release of molecules of different size (Theophylline (TPH), Vitamin B12 (Vit. B12) and Myoglobin (MGB)) from the gel and from the dried system used as a matrix for tablets was studied. The increase of weight of the tablets with and without the loaded drugs was followed together with the relative variation of the dimensions. The dry matrix, in the form of tablets was capable, during the swelling process, to incorporate a relevant amount of solvent (ca. 20 g water/g dried matrix), without dissolving in the medium, leading to a surprisingly noticeable anisotropic swelling that can be correlated with a peculiar supramolecular structure of the system induced by compression. Obtained results indicate that the new hydrogel can be suitable for sustained drug release formulations. The delivery from the matrix is deeply dependent on the size of the tested model drugs. The experimental release data obtained from the gel were satisfactorily fitted by an appropriate theoretical approach and the relative drug diffusion coefficients in the hydrogel were estimated. The release profiles of TPH, Vit. B12 and MGB from the tablets have been analyzed in terms of a new mathematical approach that allows calculating of permeability values of the loaded drugs.

Estimation of diffusion coefficient of chromium in colloidal silica using digital photography

In order to study the effectiveness of using colloidal silica, NYACOL DP5110, to stabilize chromium-contaminated soil, the diffusion of chromium in colloidal silica gel was estimated from laboratory experiments. To measure diffusion coefficients of chromium in the colloidal silica gel, a new measurement method based on digital photography was introduced. A series of experiments were designed and conducted to validate this new method and to estimate the diffusion coefficients of chromium in the colloidal silica gel. Accuracy of the proposed method was evaluated by several differentways. It was found that the apparent diffusion coefficient of chromium in colloidal silica gel ranged from 1.76 to 8.48 x 10(-10) m2/s depending mainly on the concentration of silica in the gel with chromium concentration less than 10(-2) M. Higher silica concentrations yielded lower diffusion coefficients due to the obstruction to the free movement of chromium. The adsorption isotherm of chromate to colloidal silica gel was found to be linear at pH 7; the partition coefficient was calculated to be 0.549 L/g. Mass balance calculations were performed to evaluate the accuracy of the proposed method and found that the measuring error was less than 6.5%. Based on the test data, the estimation of diffusion coefficients for chromium in colloidal silica gel using digital photography seems to be accurate and precise. This method is suitable for analyzing colored chemicals inside clear/white gels. From the results, it can be concluded that the gel behaves as a porous material with silica network forming continuous solid phase and its pore space saturated with water. The chromium ions diffuse in porous silica gel on a tortuous path. Therefore, the bulk diffusion dominates. Thus, the silica can be represented as a fix and impenetrable immersion in the solution. The presence of these motionless silica chains leads to an increase in the mean path of the diffusing molecules between two points in the system. On the basis of the test results, it can also be concluded that colloidal silica, NYACOL DP5110, for in-situ treatment of chromium-contaminated soils seems to be ineffective. Further research of more realistic simulation of diffusion and refined gel formulation with the capacity to convert the chromium to an immobile form is recommended.

In Situ Investigation of Drug Diffusion in Hydrogels by the Refractive Index Method

This work describes a simple but novel analytical method for in situ monitoring of the diffusion process of drugs in hydrogels based on refractive index measurements. The diffusion process was monitored by recording the refraction of a laser beam passing through a triangular cell, which allows the determination of changes in the refractive index distribution from the deviated distance of the linear beam. Compared to conventional methods, this new method exhibits advantages such as more simplicity, lower cost, and speed. Further, the refractive index method permits the determination of the concentration distribution of solutes in the hydrogels at any time during the diffusion process under nondestructive circumstances. The precision was determined by successfully applying this new method to the diffusion of a typical antibiotic drug, cefazolin sodium, in agarose gels of various concentrations. By employing Fick's second law, the diffusion behavior was investigated and the diffusion coefficients of cefazolin sodium in agarose gels were therefore obtained. Amsden's physical model based on obstruction effect was applied to the simulation of the diffusion process of cefazolin sodium and turned out to fit the results quite well.

Viability of Hydroxyethyl Methacrylate–Methyl Methacrylate-Microencapsulated PC12 Cells after Omental Pouch Implantation within Agarose Gels

Hydroxyethyl methacrylate-methyl methacrylate (HEMA-MMA, 75 mol% HEMA). Microcapsules containing viable PC12 cells (as an allogeneic transplant model) were implanted into omental pouches in Wistar rats. Two different capsule preparations were tested, based on differences in polymer solutions during extrusion: 10% HEMA-MMA in TEG, and 9% HEMA-MMA in TEG with 30% poly(vinyl pyrrolidone) (PVP). The omental pouch proved to be an ideal transplant site in terms of implantation, recovery, and blood vessel proximity (nutrient supply). To minimize the fibrous overgrowth and damaged capsules previously seen on implantation of individual capsules, agarose gels were used to embed the capsules before implantation. Cells proliferated within the microcapsule-agarose device during the first 7 days of implantation, but overall cell viability declined over the 3-week period, when compared with similar capsules maintained in vitro. Nonetheless, approximately 50% of the initial encapsulated cells were still viable after 3 weeks in vivo. This approach to HEMA-MMA microcapsule implantation improved cell viability and capsule integrity after 3 weeks in vivo, compared with capsules implanted without agarose.

Measurement of dye diffusion in agar gel by use of low-coherence interferometry

We demonstrate low-coherence interferometry for diffusion measurements. We have measured the diffusion coefficient of a phthalocyanine dye in 1.5% agar gel with a two-wavelength interferometer; one wavelength was matched to the absorption peak of the dye at 675 nm, while the other, 805 nm, was not affected by the dye. The diffusion coefficient of the dye was found by fitting a mathematical model for the interferometer signal to the measured low-coherence interferometry amplitude. A 95% confidence interval for the diffusion coefficient was found to be D = (2.5 +/- 0.2) x 10(-10) m2/s. The influence of speckle averaging and experiment time on the determination of the diffusion coefficient has been studied. The presented technique allows in situ characterization of diffusion in semitransparent media.

Scleroglucan/borax: characterization of a novel hydrogel system suitable for drug delivery

A new hydrogel, with scleroglucan using borax as a crosslinker, has been prepared. The physical gel has been loaded with a model molecule (theophylline) and the release of the drug from the gel was evaluated. The same system was used to prepare tablets and the delivery of theophylline in different environmental conditions (HCl and SIF) was determined. A recent theoretical approach has been applied to the dissolution profiles obtained from the tablets and a satisfactory agreement has been found with the experimental data. Furthermore, the diffusion coefficient of the model molecule was evaluated according to a suitable strategy that was tested on two set of data obtained with different set-ups (permeation and diffusion experiments). A simplified mathematical approach allows to reduce the two-dimensional problem of the Fick's second law in a one-dimensional system leading to a much easier handling of the data without loosing the accuracy of the original problem in two dimensions. The characterization of the gel has been also carried out following the kinetics of swelling in terms of water uptake.